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JEE Sequences and Series PYQs with Solutions

748 previous year questions from Sequences and Series (JEE Main & Advanced Mathematics) with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

748 questionsMathematics2006–2026Answers + solutions

About Sequences and Series PYQs

Sequences and Series has 748 previous year questions in the Quantrex Academy JEE Main & Advanced Mathematics bank. The 220 questions in this list come from JEE Main (188) and JEE Advanced (32), spanning 2006 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

Questions by year (this list)

  • 2026: 33
  • 2025: 31
  • 2024: 36
  • 2023: 47
  • 2022: 39
  • 2021: 8
  • 2020: 2
  • 2019: 1
  • 2018: 1
  • 2017: 1
  • 2016: 2
  • 2015: 2

Sequences and Series questions with solutions

1

Let α = 3+4+8+9+13+14+… upto 40 terms. If ( β)^ (α)/(1020) is a root of the equation x^2+x-2=0 , β ∈ (0, (π)/(2)) , then ^2β + 3 ^2β is equal to:

JEE Main 2026 Solution View → 2

The sum 1 + (1)/(2)(1^2 + 2^2) + (1)/(3)(1^2 + 2^2 + 3^2) + … upto 10 terms is equal to :

JEE Main 2026 Solution View → 3

The value of 1^3 - 2^3 + 3^3 - … + 15^3 is:

JEE Main 2026 Solution View → 4

The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8 . If the first term of the A.P. is equal to the common ratio of the G.P. and the

JEE Main 2026 Solution View → 5

For the functions f(θ) = α ^2θ + β ^2θ , and g(θ) = α ^2θ + β ^2θ , α > β > 0 , let _ 0 < θ < π/2 f(θ) = _ 0 < θ < π g(θ) . If the first term of a G.P. is ((α)/(2β)) , its common

JEE Main 2026 Solution View → 6

If the sum of the first 10 terms of the series (1)/(1 + 1^4 × 4) + (2)/(1 + 2^4 × 4) + (3)/(1 + 3^4 × 4) + (4)/(1 + 4^4 × 4) + … is (m)/(n) , (m, n) = 1 , then m + n is equal to :

JEE Main 2026 Solution View → 7

Let A_1, A_2, A_3, …, A_ 39 be 39 arithmetic means between the numbers 59 and 159 . Then the mean of A_ 25 , A_ 28 , A_ 31 and A_ 36 is equal to :

JEE Main 2026 Solution View → 8

Let the sum of the first n terms of an A.P. be 3n^2 + 5n . Then the sum of squares of the first 10 terms of the A.P. is:

JEE Main 2026 Solution View → 9

∑_ n=1 ^ 10 ( (528)/(n(n+1)(n+2)) ) is equal to:

JEE Main 2026 Solution View → 10

Let α=(1)/(4)+(1)/(8)+(1)/(16)+…∞ and β=(1)/(3)+(1)/(9)+(1)/(27)+…∞ . Then the value of (0.2)^ _ 5 (α) +(0.04)^ _5(β) is equal to:

JEE Main 2026 Solution View → 11

The first term of an A.P. of 30 non-negative terms is (10)/(3) . If the sum of this A.P. is the cube of its last term, then its common difference is:

JEE Main 2026 Solution View → 12

Let a_1, a_2, a_3, … be an A.P. and g_1 = a_1, g_2, g_3, … be an increasing G.P. If a_1 = a_2 + g_2 = 1 and a_3 + g_3 = 4 , then a_ 10 + g_5 is equal to:

JEE Main 2026 Solution View → 13

The sum (1^3)/(1) + (1^3 + 2^3)/(1 + 3) + (1^3 + 2^3 + 3^3)/(1 + 3 + 5) + ⋯ up to 8 terms, is:

JEE Main 2026 Solution View → 14

Let α, α + 2, α ∈ ℤ , be the roots of the quadratic equation x(x+2) + (x+1)(x+3) + (x+2)(x+4) + … + (x+n-1)(x+n+1) = 4n for some n ∈ ℕ . Then n + α is equal to :

JEE Main 2026 Solution View → 15

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and

JEE Main 2026 Solution View → 16

If ∑_ k=1 ^ n a_k = 6n^3 , then ∑_ k=1 ^ 6 ( a_ k+1 - a_k 36 )^2 is equal to _______.

JEE Main 2026 Solution View → 17

Let the arithmetic mean of 1 a and 1 ~b be (5)/(16), a>2 . If α is such that a, 4, α, ~b are in A.P., then the equation α x^ 2 -a x+2(α-2 b)=0 has:

JEE Main 2026 Solution View → 18

6 3^ 26 + 10 · 1 3^ 25 + 10 · 2 3^ 24 + 10 · 2^ 2 3^ 23 +…+ 10 · 2^ 24 3 is equal to :

JEE Main 2026 Solution View → 19

If ∑_ r=1 ^ 25 ( r r^ 4 +r^ 2 +1 )=(p)/(q) , where p and q are positive integers such that gcd(p, q)=1 , then p+q is equal to \_\_\_\_ 。

JEE Main 2026 Solution View → 20

The common difference of the A.P.: a_ 1 , a_ 2 , …, a_ m is 13 more than the common difference of the A.P.: b_ 1 , b_ 2 , …, b_ n . If b_ 31 =-277, b_ 43 =-385 and a_ 78 =327

JEE Main 2026 Solution View → 21

The value of ∑_ k=1 ^ ∞ (-1)^ k+1 ((k(k+1))/(k!)) is

JEE Main 2026 Solution View → 22

In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is ℝ-(a, b) , then a^ 2 +b^ 2 is equal to \_\_\_\_

JEE Main 2026 Solution View → 23

Let a_ 1 , a_ 2 , a_ 3 , a_ 4 be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If a_ 1 +a_ 2 +a_ 3 +a_ 4 =48 and a_ 1 a_ 2 a_ 3

JEE Main 2026 Solution View → 24

((1)/(3)+(4)/(7))+( 1 3^ 2 +(1)/(3) × (4)/(7)+ 4^ 2 7^ 2 )+( 1 3^ 3 + 1 3^ 2 × (4)/(7)+(1)/(3) × 4^ 2 7^ 2 + 4^ 3 7^ 3 )+… upto infinite terms, is equal to

JEE Main 2026 Solution View → 25

Consider an A.P.: a_ 1 , a_ 2 , …, a_ n ; a_ 1 >0 . If a_ 2 -a_ 1 =(-3)/(4), a_ n =(1)/(4) a_ 1 , and ∑_ i=1 ^ n a_ i =(525)/(2) , then ∑_ i=1 ^ 17 a_ i is equal to

JEE Main 2026 Solution View → 26

Let 729,81,9,1, … be a sequence and P_ n denote the product of the first n terms of this sequence. If 2 ∑_ n=1 ^ 40 (P_ n )^ (1)/(n) = 3^ α -1 3^ β and gcd(α, β)=1 , then α+β is

JEE Main 2026 Solution View → 27

Let ∑_ k=1 ^ n a_ k =α n^ 2 +β n . If a_ 10 =59 and a_ 6 =7 a_ 1 , then α+β is equal to

JEE Main 2026 Solution View → 28

Suppose a, b, c are in A.P. and a^ 2 , 2 ~b^ 2 , c^ 2 are in G.P. If a<b<c and a+b+c=1 , then 9(a^ 2 +b^ 2 +c^ 2 ) is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 29

If the sum of the first four terms of an A.P. is 6 and the sum of its first six terms is 4, then the sum of its first twelve terms is

JEE Main 2026 Solution View → 30

The positive integer n, for which the solutions of the equation x(x+2)+(x+2)(x+4)+⋯+(x+2 n-2)(x+2 n)=(8 n)/(3) are two consecutive even integers, is :

JEE Main 2026 Solution View → 31

Let a_ 1 , a_ 2 2 , a_ 3 2^ 2 , …, a_ 10 2^ 9 be a G.P. of common ratio 1 2 . If a_ 1 +a_ 2 +…+a_ 10 =62 , then a_ 1 is equal to :

JEE Main 2026 Solution View → 32

Let a_ 1 , a_ 2 , a_ 3 , … be G.P. of increasing positive terms such that a_ 2 · a_ 3 · a_ 4 =64 and a_ 1 +a_ 3 +a_ 5 =(813)/(7) . Then a_ 3 +a_ 5 +a_ 7 is equal to :

JEE Main 2026 Solution View → 33

Let a_ 1 =1 and for n 1, a_ n+1 =(1)/(2) a_ n + n^ 2 -2 n-1 n^ 2 (n+1)^ 2 . Then |∑_ n=1 ^ ∞ (a_ n - 2 n^ 2 ) | is equal to \_\_\_\_ .

JEE Main 2026 Solution View → 34

Let ℝ denote the set of all real numbers. Let f: ℝ arrow ℝ be a function such that f(x)>0 for all x ∈ ℝ , and f(x+y)=f(x) f(y) for all x, y ∈ ℝ . Let the real numbers a_1, a_2 …

JEE Advanced 2025 Solution View → 35

aligned & If (1)/(1^4)+(1)/(2^4)+(1)/(3^4)+… . . ∞=(π^4)/(90), & (1)/(1^4)+(1)/(3^4)+(1)/(5^4)+… . . ∞=α, & (1)/(2^4)+(1)/(4^4)+(1)/(6^4)+… . ∞=β, aligned then (α)/(β) is equal to

JEE Main 2025 Solution View → 36

Let a_ n be the n^ th term of an A. P.If S_n=a_1+a_2+a_3+…+a_n=700, a_6=7 and S_7=7 , then a_ n is equal to :

JEE Main 2025 Solution View → 37

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309 , then the sum of its first nine

JEE Main 2025 Solution View → 38

Let x_1, x_2, x_3, x_4 be in a geometric progression. 2,7,9,5 are subtracted respectively from x_1, x_2, x_3 x_4 then the resulting numbers are in an arithmetic progression. Then

JEE Main 2025 Solution View → 39

Consider two sets A and B , each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the

JEE Main 2025 Solution View → 40

If the sum of the first 20 terms of the series (4.1)/(4+3.1^2+1^4)+(4.2)/(4+3.2^2+2^4)+(4.3)/(4+3.3^2+3^4)+(4.4)/(4+3.4^2+4^4)+… is (m)/(n) , where m and n are coprime, then m+n

JEE Main 2025 Solution View → 41

1+3+5^2+7+9^2+… upto 40 terms is equal to

JEE Main 2025 Solution View → 42

Let A=\ 1,6,11,16, …\ and B=\ 9,16,23,30, …\ be the sets consisting of the first 2025 terms of two arithmetic progressions. Then n(A ∪ B) is

JEE Main 2025 Solution View → 43

The sum 1+(1+3)/(2!)+(1+3+5)/(3!)+(1+3+5+7)/(4!)+… upto ∞ terms, is equal to

JEE Main 2025 Solution View → 44

Let a_1, a_2, a_3, … be a G. P. of increasing positive numbers. If a_3 a_5=729 and a_2+a_4=(111)/(4) , then 24(a_1+a_2+a_3) is equal to

JEE Main 2025 Solution View → 45

The sum 1+3+11+25+45+71+. . upto 20 terms, is equal to

JEE Main 2025 Solution View → 46

The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by (21)/(2) . Then the number

JEE Main 2025 Solution View → 47

If the sum of the first 10 terms of the series (4.1)/(1+4.1^4)+(4.2)/(1+4.2^4)+(4.3)/(1+4.3^4)+… is (m)/(n) , where gcd(m, n)=1 , then m+n is equal to______

JEE Main 2025 Solution View → 48

Let a_1, a_2, a_3 … be in an A.P. such that ∑_ k=1 ^ 12 a_ 2 k-1 =-(72)/(5) a_1, a_1 ≠ 0 . If ∑_ k=1 ^ n a_ k =0 , then n is:

JEE Main 2025 Solution View → 49

Let a_1, a_2, …, a_ 2024 be an Arithmetic Progression such that a_1+(a_5+a_ 10 +a_ 15 +…+a_ 2020 )+a_ 2024 =2233 . Then a_1+a_2+a_3+…+a_ 2024 is equal to _______

JEE Main 2025 Solution View → 50

Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its \(11^ th \) term is :

JEE Main 2025 Solution View → 51

The value of \( _ n arrow ∞ (∑_ k=1 ^n (k^3+6 k^2+11 k+5)/((k+3)!))\) is:

JEE Main 2025 Solution View → 52

For positive integers n , if 4 a_n=(n^2+5 n+6) and S_n=∑_ k=1 ^n((1)/(a_k)) , then the value of 507 S_ 2025 is :

JEE Main 2025 Solution View → 53

The interior angles of a polygon with n sides, are in an A.P. with common difference 6^ ∘ . If the largest interior angle of the polygon is 219^ ∘ , then n is equal to

JEE Main 2025 Solution View → 54

Let T_ r be the r^ th term of an A.P. If for some m, T_ m =(1)/(25), T_ 25 =(1)/(20) , and 20 ∑_ r=1 ^ 25 T_ r =13 , then 5 m ∑_ r=m^ 2 m T_ r is equal to

JEE Main 2025 Solution View → 55

Let a_ n be a sequence such that a_0=0, a_1=(1)/(2) and 2 a_ n+2 =5 a_ n+1 -3 a_ n , n=0,1,2,3, … . Then ∑_ k=1 ^ 100 a_k is equal to

JEE Main 2025 Solution View → 56

If 7=5+(1)/(7)(5+α)+(1)/(7^2)(5+2 α)+(1)/(7^3)(5+3 α)+… ∞ , then the value of α is :

JEE Main 2025 Solution View → 57

In an arithmetic progression, if S_ 40 =1030 and S_ 12 =57 , then S_ 30 -S_ 10 is equal to :

JEE Main 2025 Solution View → 58

Let S_n=(1)/(2)+(1)/(6)+(1)/(12)+(1)/(20)+… upto n terms. If the sum of the first six terms of an A.P. with first term -p and common difference p is 2026 S_ 2025 , then the

JEE Main 2025 Solution View → 59

The number of 3 -digit numbers, that are divisible by 2 and 3 , but not divisible by 4 and 9 , is______.

JEE Main 2025 Solution View → 60

The roots of the quadratic equation 3 x^2-p x+q=0 are 10^ th and 11^ th terms of an arithmetic progression with common difference (3)/(2) . If the sum of the first 11 terms of

JEE Main 2025 Solution View → 61

If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

JEE Main 2025 Solution View → 62

Suppose that the number of terms in an A.P. is 2 k, k ∈ N . If the sum of all odd terms of the A.P. is 40 , the sum of all even terms is 55 and the last term of the A.P. exceeds

JEE Main 2025 Solution View → 63

Let a_1, a_2, a_3, … be a G.P. of increasing positive terms. If a_1 a_5=28 and a_2+a_4=29 , then a_6 is equal to:

JEE Main 2025 Solution View → 64

If ∑_ r=1 ^n T_r=((2 n-1)(2 n+1)(2 n+3)(2 n+5))/(64) , then _ n arrow ∞ ∑_ r=1 ^n((1)/(T_r)) is equal to :

JEE Main 2025 Solution View → 65

Let a, a r, a r^2 , be an infinite G.P. If ∑_ n=0 ^ ∞ a r^n=57 and ∑_ n=0 ^ ∞ a^3 r^ 3 n =9747 , then a+18 r is equal to

JEE Main 2024 Solution View → 66

If ((1)/(α+1)+(1)/(α+2)+… …+(1)/(α+1012))-((1)/(2 · 1)+(1)/(4 · 3)+(1)/(6 · 5)+… . .+(1)/(2024 · 2023))=(1)/(2024) , then α is equal to________

JEE Main 2024 Solution View → 67

If the sum of the series 1 1 ·(1+d) + 1 (1+d)(1+2 ~d) +…+ 1 (1+9 ~d)(1+10 ~d) is equal to 5 , then 50 ~d is equal to :

JEE Main 2024 Solution View → 68

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is (70)/(3) and the product of the third and fifth terms is 49 . Then the sum of

JEE Main 2024 Solution View → 69

An arithmetic progression is written in the following way The sum of all the terms of the 10^ th row is_______

JEE Main 2024 Solution View → 70

If the set R=\ (a, b): a+5 b=42, a, b ∈ ℕ\ has m elements and ∑_ n=1 ^m(1-i^ n ! )=x+i y , where i= -1 , then the value of m+x+y is

JEE Main 2024 Solution View → 71

Let the positive integers be written in the form : If the k^ th row contains exactly k numbers for every natural number k , then the row in which the number 5310 will be, is

JEE Main 2024 Solution View → 72

Let A B C be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle A B C and the same process is repeated infinitely many

JEE Main 2024 Solution View → 73

A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start of the second day, 4 more computer systems

JEE Main 2024 Solution View → 74

If S(x)=(1+x)+2(1+x)^2+3(1+x)^3+⋯+60(1+x)^ 60 , x ≠ 0 , and (60)^2 ~S(60)=a(b)^ b +b , where a, b ∈ N , then (a+b) equal to ______

JEE Main 2024 Solution View → 75

Let A=\ n ∈[100,700] ∩ ℕ: n is neither a multiple of 3 nor a multiple of 4 \ . Then the number of elements in A is

JEE Main 2024 Solution View → 76

Let the first term of a series be T_1=6 and its r^ th term T_r=3 T_ r-1 +6^r, r=2,3 , n . If the sum of the first n terms of this series is (1)/(5)(n^2-12 n+39)(4 · 6^n-5 · 3^n+1)

JEE Main 2024 Solution View → 77

For x 0 , the least value of K , for which 4^ 1+x +4^ 1-x , K 2 , 16^x+16^ -x are three consecutive terms of an A.P., is equal to :

JEE Main 2024 Solution View → 78

If 1+ 3 - 2 2 3 + 5-2 6 18 + 9 3 -11 2 36 3 + 49-20 6 180 +… upto ∞=2+( (b)/(a) +1) _e((a)/(b)) , where a and b are integers with gcd(a, b)=1 , then 11 a+18 ~b is equal to ______

JEE Main 2024 Solution View → 79

If 1 1 + 2 + 1 2 + 3 +…+ 1 99 + 100 =m and (1)/(1 · 2)+(1)/(2 · 3)+…+(1)/(99 · 100)=n , then the point (m, n) lies on the line

JEE Main 2024 Solution View → 80

Let a_1, a_2, a_3, … be in an arithmetic progression of positive terms. Let A_ k =a_1^2-a_2^2+a_3^2-a_4^2+…+a_ 2 k-1 ^2-a_ 2 k ^2 . If A_3=-153, ~A_5=-435 and a_1^2+a_2^2+a_3^2=66

JEE Main 2024 Solution View → 81

The value of (1 × 2^2+2 × 3^2+…+100 ×(101)^2)/(1^2 × 2+2^2 × 3+… .+100^2 × 101) is

JEE Main 2024 Solution View → 82

Let three real numbers a, b, c be in arithmetic progression and a+1, b, c+3 be in geometric progression. If a>10 and the arithmetic mean of a, b and c is 8, then the cube of the

JEE Main 2024 Solution View → 83

Let the first three terms 2, p and q , with q ≠ 2 , of a G.P. be respectively the 7^ th , 8^ th and 13^ th terms of an A.P. If the 5^ th term of the G.P. is the n^ th term of the

JEE Main 2024 Solution View → 84

Let S _ n denote the sum of the first n terms of an arithmetic progression. If S _ 10 = 390 and the ratio of the tenth and the fifth terms is 15: 7 , then S _ 15 - S _ 5 is equal

JEE Main 2024 Solution View → 85

If three successive terms of a G.P. with common ratio r(r > 1) are the length of the sides of a triangle and [r] denotes the greatest integer less than or equal to r, then 3 [r] +

JEE Main 2024 Solution View → 86

Let 3, 7, 11, 15, . . , 403 and 2, 5, 8, 11, . . . , 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to_________

JEE Main 2024 Solution View → 87

Let 3, a, b, c be in A . P . and 3, a - 1, b + 1, c + 9 be in G . P . Then, the arithmetic mean of a, b and c is:

JEE Main 2024 Solution View → 88

Let 2 ^ nd , 8 ^ th and 44 ^ th , terms of a non-constant A . P . be respectively the 1 ^ st , 2 ^ nd and 3 ^ rd terms of G . P . If the first term of A.P. is 1 then the sum of

JEE Main 2024 Solution View → 89

The sum of the series 1 1 - 3 ⋅ 1 ^ 2 + 1 ^ 4 + 2 1 - 3 ⋅ 2 ^ 2 + 2 ^ 4 + 3 1 - 3 ⋅ 3 ^ 2 + 3 ^ 4 + . ... up to 10 terms is

JEE Main 2024 Solution View → 90

Let a and b be two distinct positive real numbers. Let 11 ^ th term of a GP, whose first term is a and third term is b , is equal to p ^ th term of another GP, whose first term is

JEE Main 2024 Solution View → 91

Let S _ n be the sum to n-terms of an arithmetic progression 3, 7, 11, … … , if 40 < ((6)/(n ( n + 1 )) ∑ _ k = 1 ^ n S _ k ) < 42 , then n equals ____________.

JEE Main 2024 Solution View → 92

Let S _ a denote the sum of first n terms an arithmetic progression. If S _ 20 = 790 and S _ 10 = 145 , then S _ 15 - S _ 5 is :

JEE Main 2024 Solution View → 93

Let α = 1 ^ 2 + 4 ^ 2 + 8 ^ 2 + 13 ^ 2 + 19 ^ 2 + 26 ^ 2 + … … . upto 10 terms and β = ∑ _ n = 1 ^ 10 n ^ 4 . If 4α - β = 55k + 40 , then k is equal to _______.

JEE Main 2024 Solution View → 94

If _ e a, _ e b, _ e c are in an A . P . and _ e a - _ e 2b, _ e 2b - _ e 3c, _ e 3c - _ e a are also in an A . P . , then a: b: c is equal to

JEE Main 2024 Solution View → 95

If each term of a geometric progression a _ 1 , a _ 2 , a _ 3 , … with a _ 1 = (1)/(8) and a _ 2 ≠ a _ 1 , is the arithmetic mean of the next two terms and S _ n = a _ 1 + a _ 2 +

JEE Main 2024 Solution View → 96

In an A.P., the sixth term a _ 6 = 2 . If the a _ 1 a _ 4 a _ 5 is the greatest, then the common difference of the A.P., is equal to

JEE Main 2024 Solution View → 97

If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of the G.P, then the common ratio of the G.P. is equal to

JEE Main 2024 Solution View → 98

The 20 ^ th term from the end of the progression 20, 19(1)/(4), 18(1)/(2), 17(3)/(4), … , - 129(1)/(4) is :-

JEE Main 2024 Solution View → 99

The number of common terms in the progressions 4, 9, 14, 19, … … , up to 25 ^ th term and 3, 6, 9, 12 ,.... up to 37 ^ th term is :

JEE Main 2024 Solution View → 100

If 8 = 3 + (1)/(4)(3 + p) + 1 4 ^ 2 (3 + 2p) + 1 4 ^ 3 (3 + 3p) + … ∞ , then the value of p is

JEE Main 2024 Solution View → 101

Let r 7 ⏞ 5 … 5 7 denote the (r + 2) digit number where the first and the last digits are 7 and the remaining r digits are 5 . Consider the sum S = 77 + 757 + 7557 + … + 98 7 ⏞ 5

JEE Advanced 2023 Solution View → 102

Let A _ 1 and A _ 2 be two arithmetic means and G _ 1 , G _ 2 and G _ 3 be three geometric means of two distinct positive numbers. Then G _ 1 ^ 4 + G _ 2 ^ 4 + G _ 3 ^ 4 + G _ 1 ^

JEE Main 2023 Solution View → 103

If the sum of the series ((1)/(2) - (1)/(3)) + ( 1 2 ^ 2 - (1)/(2 · 3) + 1 3 ^ 2 ) + ( 1 2 ^ 3 - 1 2 ^ 2 · 3 + 1 2 · 3 ^ 2 - 1 3 ^ 3 ) + ( 1 2 ^ 4 - 1 2 ^ 3 · 3 + 1 2 ^ 2 · 3 ^ 2

JEE Main 2023 Solution View → 104

Let a _ 1 , a _ 2 , a _ 3 , … . be a G.P. of increasing positive numbers. Let the sum of its 6 ^ th and 8 ^ th terms be 2 and the product of its 3 ^ rd and 5 ^ th terms be (1)/(9)

JEE Main 2023 Solution View → 105

Let [α] denote the greatest integer ≤ α . Then [ 1 ] + [ 2 ] + [ 3 ] + . . . . . . . . . . . . . + [ 120 ] is equal to

JEE Main 2023 Solution View → 106

Let f(x) = ∑ _ k = 1 ^ 10 k · x ^ k , x ∈ ℝ , if 2f(2) + f ^ ' (2) = 119 (2) ^ n + 1 then n is equal to ______.

JEE Main 2023 Solution View → 107

Let s _ 1 , s _ 2 , s _ 3 . . . . , s _ 10 respectively be the sum of 12 terms of 10A . Ps whose first terms are 1, 2, 3, . . . . , 10 and the common differences are 1, 3, 5, . .

JEE Main 2023 Solution View → 108

The sum to 20 terms of the series 2 · 2 ^ 2 - 3 ^ 2 + 2 · 4 ^ 2 - 5 ^ 2 + 2 · 6 ^ 2 - . . . . . . . . . . . . is equal to __________ .

JEE Main 2023 Solution View → 109

Let be a sequence such that a _ 1 + a _ 2 + . . . + a _ n = n ^ 2 + 3n (n + 1)(n + 2) . If 28 ∑ _ k = 1 ^ 10 1 a _ k = p _ 1 p _ 2 p _ 3 . . . p _ m , where p _ 1 , p _ 2 , . . .

JEE Main 2023 Solution View → 110

Let a, b, c and d be positive real numbers such that a + b + c + d = 11 . If the maximum value of a ^ 5 b ^ 3 c ^ 2 d is 3750β , then the value of β is

JEE Main 2023 Solution View → 111

For k ∈ ℕ , if the sum of the series 1 + (4)/(k) + 8 k ^ 2 + 13 k ^ 3 + 19 k ^ 4 + . . . . . . is 10 , then the value of k is

JEE Main 2023 Solution View → 112

Let x _ 1 , x _ 2 , … , x _ 100 be in an arithmetic progression, with x _ 1 = 2 and their mean equal to 200 . If y _ i = i( x _ i - i), 1 ≤ i ≤ 100 , then the mean of y _ 1 , y _

JEE Main 2023 Solution View → 113

Let S = 109 + (108)/(5) + 107 5 ^ 2 + … . + 2 5 ^ 107 + 1 5 ^ 108 . Then the value of (16S - ( 25 ) ^ - 54 ) is equal to

JEE Main 2023 Solution View → 114

If S _ n = 4 + 11 + 21 + 34 + 50 + … to n terms, then (1)/(60)( S _ 29 - S _ 9 ) is equal to

JEE Main 2023 Solution View → 115

Suppose a _ 1 , a _ 2 , 2, a _ 3 , a _ 4 be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms

JEE Main 2023 Solution View → 116

Let the first term a and the common ratio r of a geometric progression be positive integers. If the sum of squares of its first three terms is 33033 , then the sum of these three

JEE Main 2023 Solution View → 117

The sum of all those terms, of the arithmetic progression 3, 8, 13, . . . , 373 , which are not divisible by 3 , is equal to ________.

JEE Main 2023 Solution View → 118

Let a _ n be n ^ th term of the series 5 + 8 + 14 + 23 + 35 + 50 + . . . . . . . and S _ n = ∑ _ k = 1 ^ n a _ k . Then S _ 30 - a _ 40 is equal to

JEE Main 2023 Solution View → 119

Let 0 < z < y < x be three real numbers such that (1)/(x), (1)/(y), (1)/(z) are in an arithmetic progression and x, 2 y, z are in a geometric progression. If xy + yz + zx = 3 2

JEE Main 2023 Solution View → 120

Let S _ K = (1 + 2 + . . . + K)/(K) and ∑ _ j = 1 ^ n S ^ 2 j = (n)/(A)(B n ^ 2 + Cn + D) where A, B, C, D ∈ N and A Has least value then

JEE Main 2023 Solution View → 121

If gcd(m, n) = 1 and 1 ^ 2 - 2 ^ 2 + 3 ^ 2 - 4 ^ 2 + . . . . + (2021) ^ 2 - (2022) ^ 2 + (2023) ^ 2 = 1012 m ^ 2 n then m ^ 2 - n ^ 2 is equal to

JEE Main 2023 Solution View → 122

If (20) ^ 19 + 2(21) (20) ^ 18 + 3 (21) ^ 2 (20) ^ 17 + . . . + 20 (21) ^ 19 = k (20) ^ 19 , then k is equal to _____.

JEE Main 2023 Solution View → 123

The sum of the first 20 terms of the series 5 + 11 + 19 + 29 + 41 + . . . is

JEE Main 2023 Solution View → 124

Let a _ 1 , a _ 2 , a _ 3 , . . . . , a _ n be n positive consecutive terms of an arithmetic progression. If d > 0 is its common difference, then _ n → ∞ (d)/(n) ( 1 a _ 1 + a _ 2

JEE Main 2023 Solution View → 125

The sum ∑ _ n = 1 ^ ∞ 2 n ^ 2 + 3n + 4 ( 2n ) ! is equal to :

JEE Main 2023 Solution View → 126

The sum of the common terms of the following three arithmetic progressions. 3, 7, 11, 15, … … … … , 399 2, 5, 8, 11, . . . . . . . . . 359 and 2, 7, 12, 17, … … , 197 , is equal

JEE Main 2023 Solution View → 127

The sum to 10 terms of the series 1 1 + 1 ^ 2 + 1 ^ 4 + 2 1 + 2 ^ 2 + 2 ^ 4 + 3 1 + 3 ^ 2 + 3 ^ 4 + … is :-

JEE Main 2023 Solution View → 128

Let a _ 1 = 8, a _ 2 , a _ 3 , … . a _ n be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms

JEE Main 2023 Solution View → 129

The number of 3 -digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is _____ .

JEE Main 2023 Solution View → 130

Let a _ 1 , a _ 2 , a _ 3 , … … . be an A.P. If a _ 7 = 3 , the product ( a _ 1 a _ 4 ) is minimum and the sum of its first n terms is zero then n ! - 4 a _ n(n + 2) is equal to

JEE Main 2023 Solution View → 131

The sum 1 ^ 2 - 2 . 3 ^ 2 + 3 . 5 ^ 2 - 4 . 7 ^ 2 + 5 . 9 ^ 2 - … . . + 15 . 29 ^ 2 is _____ .

JEE Main 2023 Solution View → 132

If the sum and product of four positive consecutive terms of a G.P., are 126 and 1296 , respectively, then the sum of common ratios of all such GPs is

JEE Main 2023 Solution View → 133

Let a _ 1 , a _ 2 , … … , a _ n be in A.P. If a _ 5 = 2 a _ 7 and a _ 11 = 18 , then 12( 1 a _ 10 + a _ 11 + 1 a _ 11 + a _ 12 + … . . 1 a _ 17 + a _ 18 ) is equal to _____ .

JEE Main 2023 Solution View → 134

Number of 4 -digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to _____ .

JEE Main 2023 Solution View → 135

Let a, b, c > 1, a ^ 3 , b ^ 3 and c ^ 3 be in A . P . and _ a b , _ c a and _ b c be in G . P . If the sum of first 20 terms of an A . P . , whose first term is (a + 4b + c)/(3)

JEE Main 2023 Solution View → 136

The 8 ^ th common term of the series S _ 1 = 3 + 7 + 11 + 15 + 19 + … S _ 2 = 1 + 6 + 11 + 16 + 21 + … . is

JEE Main 2023 Solution View → 137

If a _ n = - 2 4 n ^ 2 - 16n + 15 , then a _ 1 + a _ 2 + … . + a _ 25 is equal to:

JEE Main 2023 Solution View → 138

∑ _ n = 0 ^ ∞ n ^ 3 ( ( 2n ) ! ) + ( 2n - 1 ) ( n ! ) ( n ! ) ( ( 2n ) ! ) = ae + (b)/(e) + c where a, b, c ∈ ℤ and e = ∑ _ n = 0 ^ ∞ (1)/(n !) Then a ^ 2 - b + c is equal to

JEE Main 2023 Solution View → 139

Let a _ 1 = b _ 1 = 1 and a _ n = a _ n - 1 + ( n - 1 ) , b _ n = b _ n - 1 + a _ n - 1 , ∀ n ≥ 2 . If S = ∑ _ n = 1 ^ 10 ( b _ n 2 ^ n ) and T = ∑ _ n = 1 ^ 8 n 2 ^ n - 1 then 2

JEE Main 2023 Solution View → 140

Let \ a_k\ and \ b_k\ , k ∈ ℕ , be two G.P.s with common ratio r_1 and r_2 respectively such that a_1=b_1=4 and r_1<r_2 . Let c_ k =a_ k +b_ k , k ∈ ℕ . If c_2=5 and c_3=(13)/(4)

JEE Main 2023 Solution View → 141

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48 , is

JEE Main 2023 Solution View → 142

Let a _ 1 , a _ 2 , a _ 3 , … . be a GP of increasing positive numbers. If the product of fourth and sixth terms is 9 and the sum of fifth and seventh terms is 24 , then a _ 1 a _

JEE Main 2023 Solution View → 143

For the two positive numbers a, b , if a, b and (1)/(18) are in a geometric progression, while (1)/(a), 10 and (1)/(b) are in an arithmetic progression, then, 16a + 12b is equal

JEE Main 2023 Solution View → 144

Let A _ 1 , A _ 2 , A _ 3 be the three A.P. with the same common difference d and having their first terms as A, A + 1, A + 2 , respectively. Let a, b, c be the 7 ^ th , 9 ^ th

JEE Main 2023 Solution View → 145

If 1 ^ 3 + 2 ^ 3 + 3 ^ 3 . . . . . . uptonterms 1 · 3 + 2 · 5 + 3 · 7 + . . . . uptonterms = (9)/(5) then the value of n is

JEE Main 2023 Solution View → 146

For three positive integers p, q, r , x ^ p q ^ 2 = y ^ qr = z ^ p ^ 2 r and r = pq + 1 such that 3, 3 _ y x, 3 _ z y, 7 _ x z are in A.P. with common difference (1)/(2) . The r

JEE Main 2023 Solution View → 147

The 4 th term of GP is 500 and its common ratio is (1)/(m), m ∈ N . Let S _ n denote the sum of the first n terms of this GP. If S _ 6 > S _ 5 + 1 and S _ 7 < S _ 6 + (1)/(2)

JEE Main 2023 Solution View → 148

Let l _ 1 , l _ 2 . . . l _ 100 be consecutive terms of an arithmetic progression with common difference d _ 1 , and let w _ 1 , w _ 2 , … , w _ 100 be consecutive terms of

JEE Advanced 2022 Solution View → 149

Let a _ 1 , a _ 2 , a _ 3 , … be an arithmetic progression with a _ 1 = 7 and common difference 8 . Let T _ 1 , T _ 2 , T _ 3 , … be such that T _ 1 = 3 and T _ n + 1 - T _ n = a

JEE Advanced 2022 Solution View → 150

Let \ a _ n \ _ n = 0 ^ ∞ be a sequence such that a _ 0 = a _ 1 = 0 and a _ n + 2 = 3 a _ n + 1 - 2 a _ n + 1, ∀ n ≥ 0 . Then a _ 25 a _ 23 - 2 a _ 25 a _ 22 - 2 a _ 23 a _ 24 + 4

JEE Main 2022 Solution View → 151

∑ _ r = 1 ^ 20 ( r ^ 2 + 1)(r !) is equal to

JEE Main 2022 Solution View → 152

If (1)/((20 - a)(40 - a)) + (1)/((40 - a)(60 - a)) + … … + (1)/((180 - a)(200 - a)) = (1)/(256) , then the maximum value of a is

JEE Main 2022 Solution View → 153

Let a _ 1 , a _ 2 , a _ 3 , … be an A.P. If ∑ _ r = 1 ^ ∞ a _ r 2 ^ r = 4 , then 4 a _ 2 is equal to ______.

JEE Main 2022 Solution View → 154

If (1)/(2 × 3 × 4) + (1)/(3 × 4 × 5) + (1)/(4 × 5 × 6) + … + (1)/(100 × 101 × 102) = (k)/(101) , then 34k is equal to _______.

JEE Main 2022 Solution View → 155

If 6 3 ^ 12 + 10 3 ^ 11 + 20 3 ^ 10 + 40 3 ^ 9 + … . . + (10240)/(3) = 2 ^ n · m , where m is odd, then m . n is equal to _____ .

JEE Main 2022 Solution View → 156

If the minimum value of f(x) = 5 x ^ 2 2 + α x ^ 5 , x > 0 , is 14 , then the value of α is equal to

JEE Main 2022 Solution View → 157

Consider the sequence a _ 1 , a _ 2 , a _ 3 , … … such that a _ 1 = 1, a _ 2 = 2 and a _ n + 2 = 2 a _ n + 1 + a _ n for n = 1, 2, 3, … If ( a _ 1 + 1 a _ 2 a _ 3 ) · ( a _ 2 + 1

JEE Main 2022 Solution View → 158

For p, q ∈ R , consider the real valued function f(x) = (x - p) ^ 2 - q, x ∈ R and q > 0 . Let a _ 1 , a _ 2 , a _ 3 and a _ 4 be in an arithmetic progression with mean p and

JEE Main 2022 Solution View → 159

Let x _ 1 , x _ 2 , x _ 3 , … . . , x _ 20 be in geometric progression with x _ 1 = 3 and the common ration (1)/(2) . A new data is constructed replacing each x _ i by ( x _ i

JEE Main 2022 Solution View → 160

Let the sum of an infinite G . P . , whose first term is a and the common ratio is r , be 5 . Let the sum of its first five terms be (98)/(25) . Then the sum of the first 21 terms

JEE Main 2022 Solution View → 161

2 ^ 3 - 1 ^ 3 1 × 7 + 4 ^ 3 - 3 ^ 3 + 2 ^ 3 - 1 ^ 3 2 × 11 + 6 ^ 3 - 5 ^ 3 + 4 ^ 3 - 3 ^ 3 + 2 ^ 3 - 1 ^ 3 3 × 15 + … . . + 30 ^ 3 - 29 ^ 3 + 28 ^ 3 - 27 ^ 3 + … + 2 ^ 3 - 1 ^ 3

JEE Main 2022 Solution View → 162

Suppose a _ 1 , a _ 2 , … , a _ n , … be an arithmetic progression of natural numbers. If the ratio of the sum of the first five terms to the sum of first nine terms of the

JEE Main 2022 Solution View → 163

Let f(x) = 2 x ^ 2 - x - 1 and S = \ n ∈ ℤ: |f(n)| ≤ 800\ . Then, the value of ∑ _ n ∈ S f(n) is equal to _______.

JEE Main 2022 Solution View → 164

If ∑ _ k = 1 ^ 10 k k ^ 4 + k ^ 2 + 1 = (m)/(n) , where m and n are co-prime, then m + n is equal to

JEE Main 2022 Solution View → 165

Different A.P.&#39;s are constructed with the first term 100 , the last term 199 , And integral common differences. The sum of the common differences of all such, A.P&#39;s having

JEE Main 2022 Solution View → 166

Consider two G.Ps. 2, 2 ^ 2 , 2 ^ 3 , … and 4, 4 ^ 2 , 4 ^ 3 , … of 60 and n terms respectively. If the geometric mean of all the 60 + n terms is (2)(225)/(8) , then ∑ _ k = 1 ^ n

JEE Main 2022 Solution View → 167

The series of positive multiples of 3 is divided into sets : \ 3\ , \ 6, 9, 12\ , \ 15, 18, 21, 24, 27\ , … Then the sum of the elements in the 11 ^ th set is equal to _______.

JEE Main 2022 Solution View → 168

The sum ∑ _ n = 1 ^ 21 (3)/((4n - 1)(4n + 3)) is equal to

JEE Main 2022 Solution View → 169

Let a _ 1 = b _ 1 = 1, a _ n = a _ n - 1 + 2 and b _ n = a _ n + b _ n - 1 for every natural number n ≥ 2 . Then ∑ _ n = 1 ^ 15 a _ n · b _ n is equal to _____ .

JEE Main 2022 Solution View → 170

The sum of the infinite series 1 + (5)/(6) + 12 6 ^ 2 + 22 6 ^ 3 + 35 6 ^ 4 + 51 6 ^ 5 + 70 6 ^ 6 + … is equal to:

JEE Main 2022 Solution View → 171

Let 3, 6, 9, 12, … upto 78 terms and 5, 9, 13, 17, … upto 59 terms be two series. Then, the sum of the terms common to both the series is equal to ______.

JEE Main 2022 Solution View → 172

Let \ a _ n \ _ n = 0 ^ ∞ be a sequence such that a _ 0 = a _ 1 = 0 and a _ n + 2 = 2 a _ n + 1 - a _ n + 1 for all n ≥ 0 . Then, ∑ _ n = 2 ^ ∞ a _ n 7 ^ n is equal to

JEE Main 2022 Solution View → 173

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1: 7 and a + n = 33 , then the value of n is

JEE Main 2022 Solution View → 174

Let for n = 1, 2, … … , 50, S _ n be the sum of the infinite geometric progression whose first term is n ^ 2 and whose common ratio is 1 (n + 1) ^ 2 . Then the value of (1)/(26) +

JEE Main 2022 Solution View → 175

Let A _ 1 , A _ 2 , A _ 3 , … … be an increasing geometric progression of positive real numbers. If A _ 1 A _ 3 A _ 5 A _ 7 = (1)/(1296) and A _ 2 + A _ 4 = (7)/(36) , then, the

JEE Main 2022 Solution View → 176

Let S = 2 + (6)/(7) + 12 7 ^ 2 + 20 7 ^ 3 + 30 7 ^ 4 + … . . then 4S is equal to

JEE Main 2022 Solution View → 177

If a _ 1 , a _ 2 , a _ 3 … and b _ 1 , b _ 2 , b _ 3 … . are A.P. and a _ 1 = 2, a _ 10 = 3, a _ 1 b _ 1 = 1 = a _ 10 b _ 10 then a _ 4 b _ 4 is equal to

JEE Main 2022 Solution View → 178

If x = ∑ _ n = 0 ^ ∞ a ^ n , y = ∑ _ n = 0 ^ ∞ b ^ n , z = ∑ _ n = 0 ^ ∞ c ^ n , where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1 , abc ≠ 0 , then

JEE Main 2022 Solution View → 179

If the sum of the first ten terms of the series (1)/(5) + (2)/(65) + (3)/(325) + (4)/(1025) + (5)/(2501) + … . is (m)/(n) , where m and n are co-prime numbers, then m + n is equal

JEE Main 2022 Solution View → 180

If A = ∑ _ n = 1 ^ ∞ 1 (3 + (- 1) ^ n ) ^ n and B = ∑ _ n = 1 ^ ∞ (- 1) ^ n (3 + (- 1) ^ n ) ^ n , then (A)/(B) is equal to

JEE Main 2022 Solution View → 181

If a _ 1 ( > 0 ) , a _ 2 , a _ 3 , a _ 4 , a _ 5 are in a G.P. , a _ 2 + a _ 4 = 2 a _ 3 + 1 and 3 a _ 2 + a _ 3 = 2 a _ 4 , then a _ 2 + a _ 4 + 2 a _ 5 is equal to _____.

JEE Main 2022 Solution View → 182

Let A = ∑ _ i = 1 ^ 10 ∑ _ j = 1 ^ 10 min\ i, j\ and B = ∑ _ i = 1 ^ 10 ∑ _ j = 1 ^ 10 max\ i, j\ . Then A + B is equal to _____.

JEE Main 2022 Solution View → 183

The sum 1 + 2 · 3 + 3 · 3 ^ 2 + … … . . + 10 · 3 ^ 9 is equal to

JEE Main 2022 Solution View → 184

The greatest integer less than or equal to the sum of first 100 terms of the sequence (1)/(3), (5)/(9), (19)/(27), (65)/(81), … is equal to ______

JEE Main 2022 Solution View → 185

Let x, y > 0 . If x ^ 3 y ^ 2 = 2 ^ 15 , then the least value of 3x + 2y is

JEE Main 2022 Solution View → 186

If \ a _ i \ _ i = 1 ^ n , where n is an even integer, is an arithmetic progression with common difference 1 , and ∑ _ i = 1 ^ n a _ i = 192, ∑ _ i = 1 ^ (n)/(2) a _ 2i = 120

JEE Main 2022 Solution View → 187

Paragraph: Let M=\ (x, y) ∈ ℝ × ℝ: x^ 2 +y^ 2 ≤ r^ 2 \ , where r>0 . Consider the geometric progression a_ n = 1 2^ n-1 , n=1,2,3, … . Let S_ 0 =0 and, for n ≥ 1 , let S_ n denote

JEE Advanced 2021 Solution View → 188

Paragraph: Let M=\ (x, y) ∈ ℝ × ℝ: x^ 2 +y^ 2 ≤ r^ 2 \ , where r>0 . Consider the geometric progression a_ n = 1 2^ n-1 , n=1,2,3, … . Let S_ 0 =0 and, for n ≥ 1 , let S_ n denote

JEE Advanced 2021 Solution View → 189

Let S _ n = 1 · ( n - 1 ) + 2 · ( n - 2 ) + 3 · ( n - 3 ) + … + ( n - 1 ) · 1, n ⩾ 4 . The sum ∑ _ n = 4 ^ ∞ ( 2 S _ n n ! - (1)/(( n - 2 ) !))is equal to :

JEE Main 2021 Solution View → 190

Let a _ 1 , a _ 2 , … , a _ 21 be an A . P . such that ∑ _ n = 1 ^ 20 1 a _ n a _ n + 1 = (4)/(9) . If the sum of this A . P . is 189, then a _ 6 a _ 16 is equal to :

JEE Main 2021 Solution View → 191

Let a _ 1 , a _ 2 , a _ 3 , … be an A.P. If a _ 1 + a _ 2 + … + a _ 10 a _ 1 + a _ 2 + … + a _ p = 100 p ^ 2 , p ≠ 10, then a _ 11 a _ 10 is equal to :

JEE Main 2021 Solution View → 192

If S = (7)/(5) + 9 5 ^ 2 + 13 5 ^ 3 + 19 5 ^ 4 + … , then 160S is equal to .

JEE Main 2021 Solution View → 193

The sum of 10 terms of the series 3 1 ^ 2 × 2 ^ 2 + 5 2 ^ 2 × 3 ^ 2 + 7 3 ^ 2 × 4 ^ 2 + … is :

JEE Main 2021 Solution View → 194

Three numbers are in an increasing geometric progression with common ratio r . If the middle number is doubled, then the new numbers are in an arithmetic progression with common

JEE Main 2021 Solution View → 195

Let m be the minimum possible value of _ 3 ( 3 ^ y _ 1 + 3 ^ y _ 2 + 3 ^ y _ 3 ) , where y _ 1 , y _ 2 , y _ 3 are real numbers for which y _ 1 + y _ 2 + y _ 3 = 9 . Let M be the

JEE Advanced 2020 Solution View → 196

Let a _ 1 , a _ 2 , a _ 3 , . . . . . . . . . be a sequence of positive integers in arithmetic progression with common difference 2 . Also, let b _ 1 , b _ 2 , b _ 3 , . . . . . .

JEE Advanced 2020 Solution View → 197

Let AP(a; d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d > 0 . If AP(1; 3) ∩ AP(2; 5) ∩ AP(3; 7) = AP(a; d)

JEE Advanced 2019 Solution View → 198

Let X be the set consisting of the first 2018 terms of the arithmetic progression 1,6, 11, … , and Y be the set consisting of the first 2018 terms of the arithmetic progression

JEE Advanced 2018 Solution View → 199

The sides of a right-angled triangle are in arithmetic progression. If the triangle has area 24 square units, then what is the length of its smallest side?

JEE Advanced 2017 Solution View → 200

The value of ∑ _ k = 1 ^ 13 (1)/(sin ⁡ ((π)/(4) + ((k - 1)π)/(6))sin ⁡ ((π)/(4) + (kπ)/(6))) is equal to

JEE Advanced 2016 Solution View →
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Application of Derivatives (795)Three Dimensional Geometry (756)Functions (700)Definite Integration (692)Vector Algebra (616)Differential Equations (586)Continuity and Differentiability (576)Probability (561)Complex Number (551)Binomial Theorem (550)Quadratic Equation (517)Determinants (508)

Sequences and Series in other exams

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