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Sequences and Series — JEE Main & Advanced Mathematics PYQs

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

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1

Let = 3+4+8+9+13+14+ upto 40 terms. If ( )^ 1020 is a root of the equation x^2+x-2=0 , (0, 2 ) , then ^2 + 3 ^2 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:

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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( ) = ^2 + ^2 , and g( ) = ^2 + ^2 , > > 0 , let _ 0 < < /2 f( ) = _ 0 < < g( ) . If the first term of a G.P. is ( 2 ) , its common ratio is ( 2 ) and the sum of

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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 A₁, A₂, A₃, , A₃₉ be 39 arithmetic means between the numbers 59 and 159 . Then the mean of A₂₅, A₂₈, A₃₁ and A₃₆ 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 = 1 4 + 1 8 + 1 16 + and = 1 3 + 1 9 + 1 27 + . Then the value of (0.2)^ _ 5 ( ) +(0.04)^ ₅( ) 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 a₁, a₂, a₃, be an A.P. and g₁ = a₁, g₂, g₃, be an increasing G.P. If a₁ = a₂ + g₂ = 1 and a₃ + g₃ = 4 , then a₁₀ + g₅ 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:

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Let , + 2, 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 + 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 th

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

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Let the arithmetic mean of 1 a and 1 ~b be 5 16 , a >2 . If is such that a , 4, , ~b are in A.P., then the equation x²-a x+2( -2 b)=0 has:

JEE Main 2026 Solution View → 18

6 3²⁶ + 10 1 3²⁵ + 10 2 3²⁴ + 10 2² 3²³ + + 10 2²⁴ 3 is equal to :

JEE Main 2026 Solution View → 19

If _ r=1 ²⁵ ( r r⁴+r²+1 )= p q , where p and q are positive integers such that gcd (p, q)=1 , then p+q is equal to _ _ _ _ 。

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The common difference of the A.P.: a₁, a₂, , a_ m is 13 more than the common difference of the A.P.: b₁, b₂, , b_ n . If b₃₁=-277, b₄₃=-385 and a₇₈=327 , then a₁ is equal to

JEE Main 2026 Solution View → 21

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

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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 a²+b² is equal to _ _ _ _ .

JEE Main 2026 Solution View → 23

Let a₁, a₂, a₃, a₄ be an A.P. of four terms such that each term of the A.P. and its common difference l are integers. If a₁+a₂+a₃+a₄=48 and a₁ a₂ a₃ a₄+l⁴=361 , then the largest te

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( 1 3 + 4 7 )+ ( 1 3² + 1 3 4 7 + 4² 7² )+ ( 1 3³ + 1 3² 4 7 + 1 3 4² 7² + 4³ 7³ )+ upto infinite terms, is equal to

JEE Main 2026 Solution View → 25

Consider an A.P.: a₁, a₂, , a_ n ; a₁>0 . If a₂-a₁= -3 4 , a_ n = 1 4 a₁ , 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^ -1 3^ and gcd ( , )=1 , then + is equal to

JEE Main 2026 Solution View → 27

Let _ k=1 ^ n a_ k = n²+ n . If a₁₀=59 and a₆=7 a₁ , then + 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 a₁, a₂ 2 , a₃ 2² , , a₁₀ 2⁹ be a G.P. of common ratio 1 2 . If a₁+a₂+ +a₁₀=62 , then a₁ is equal to :

JEE Main 2026 Solution View → 32

Let a₁, a₂, a₃, be G.P. of increasing positive terms such that a₂ a₃ a₄=64 and a₁+a₃+a₅= 813 7 . Then a₃+a₅+a₇ is equal to :

JEE Main 2026 Solution View → 33

Let a₁=1 and for n 1, a_ n+1 = 1 2 a_ n + n²-2 n-1 n²(n+1)² . Then | _ n=1 ^ (a_ n - 2 n² ) | is equal to _ _ _ _ .

JEE Main 2026 Solution View → 34

Let R denote the set of all real numbers. Let f: R 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 , a ₅₀ be in a

JEE Advanced 2025 Solution View → 35

aligned & If 1 1^4 + 1 2^4 + 1 3^4 + . . = ^4 90 , & 1 1^4 + 1 3^4 + 1 5^4 + . . = , & 1 2^4 + 1 4^4 + 1 6^4 + . = , aligned then is equal to

JEE Main 2025 Solution View → 36

Let a _ n be the n ^ th term of an A. P. If S_n=a₁+a₂+a₃+ +a_n=700, a₆=7 and S₇=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 term

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 x₁, x₂, x₃x₄ then the resulting numbers are in an arithmetic progression. Then the va

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 eleme

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 is equal to :-

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 a₁, a₂, a₃, be a G. P. of increasing positive numbers. If a ₃ a ₅=729 and a ₂+ a ₄= 111 4 , then 24 (a₁+a₂+a₃ ) 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 of te

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 a₁, a₂, a₃ 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 a₁, a₂, , a₂₀₂₄ be an Arithmetic Progression such that a₁+ (a₅+a₁₀+a₁₅+ +a₂₀₂₀ )+a₂₀₂₄=2233 . Then a₁+a₂+a₃+ +a₂₀₂₄ 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 ( _ k=1 ^n k^3+6 k^2+11 k+5 (k+3)! ) ) is:

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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 S₂₀₂₅ 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

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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

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Let a_ n be a sequence such that a₀=0, a₁= 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+ )+ 1 7^2 (5+2 )+ 1 7^3 (5+3 )+ , then the value of is :

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In an arithmetic progression, if S₄₀=1030 and S₁₂=57 , then S₃₀-S₁₀ is equal to :

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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 absolute differe

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 this

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 the

JEE Main 2025 Solution View → 63

Let a₁, a₂, a₃, be a G.P. of increasing positive terms. If a₁ a₅=28 and a₂+a₄=29 , then a₆ 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 _ 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 +1 + 1 +2 + + 1 +1012 )- ( 1 2 1 + 1 4 3 + 1 6 5 + . .+ 1 2024 2023 )= 1 2024 , then 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 the 4^

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_______

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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 ______

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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 time

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 cr

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 T₁=6 and its r^ th term T_r=3 T_ r-1 +6^r, r=2,3 , . 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 ) , then

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 a₁, a₂, a₃, 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

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 ge

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 A.P

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 to:

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 + − r i

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 first 20 terms

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 a an

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 4 α - β = 55 k + 40 , then k is equal to _______.

JEE Main 2024 Solution View → 94

If log e a , log e b , log e c are in an A . P . and log e a - log e 2 b , log e 2 b - log e 3 c , log e 3 c - log 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 + … + a n , then S 20 -

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 + 2 p + 1 4 3 3 + 3 p + … ∞ , then the value of p is

JEE Main 2024 Solution View → 101

Let 7 5 &#8230; 5 &#9182; 7 r 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 + &#82

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 2 G 3 2 is equal to

JEE Main 2023 Solution View → 103

If the sum of the series 1 2 - 1 3 + 1 2 2 - 1 2 &#183; 3 + 1 3 2 + 1 2 3 - 1 2 2 &#183; 3 + 1 2 &#183; 3 2 - 1 3 3 + 1 2 4 - 1 2 3 &#183; 3 + 1 2 2 &#183; 3 2 - 1 2 &#183; 3 3 + 1

JEE Main 2023 Solution View → 104

Let a 1 , a 2 , a 3 , &#8230; . 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 . Then 6 a 2

JEE Main 2023 Solution View → 105

Let &#945; denote the greatest integer &#8804; &#945; . Then 1 + 2 + 3 + . . . . . . . . . . . . . + 120 is equal to

JEE Main 2023 Solution View → 106

Let f x = &#8721; k = 1 10 k &#183; x k , x &#8712; &#8477; , if 2 f 2 + f &#39; 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 10 A . 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 &#183; 2 2 - 3 2 + 2 &#183; 4 2 - 5 2 + 2 &#183; 6 2 - . . . . . . . . . . . . is equal to _ _ _ _ _ _ _ _ _ _ .

JEE Main 2023 Solution View → 109

Let &#60; a n &#62; be a sequence such that a 1 + a 2 + . . . + a n = n 2 + 3 n n + 1 n + 2 . If 28 &#8721; k = 1 10 1 a k = p 1 p 2 p 3 . . . p m , where p 1 , p 2 , . . . p m are

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 3750 &#946; , then the value of &#946; is

JEE Main 2023 Solution View → 111

For k &#8712; &#8469; , 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 , &#8230; , 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 &#8804; i &#8804; 100 , then the mean of y 1 , y

JEE Main 2023 Solution View → 113

Let S = 109 + 108 5 + 107 5 2 + &#8230; . + 2 5 107 + 1 5 108 . Then the value of 16 S - ( 25 ) - 54 is equal to

JEE Main 2023 Solution View → 114

If S n = 4 + 11 + 21 + 34 + 50 + &#8230; 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 of the

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 t

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 = &#8721; k = 1 n a k . Then S 30 - a 40 is equal to

JEE Main 2023 Solution View → 119

Let 0 &#60; z &#60; y &#60; 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 x y + y z + z x =

JEE Main 2023 Solution View → 120

Let S K = 1 + 2 + . . . + K K and &#8721; j = 1 n S 2 j = n A B n 2 + C n + D where A , B , C , D &#8712; N and A Has least value then

JEE Main 2023 Solution View →
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