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Sequences and Series — NDA Mathematics PYQs

182 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.

182 questionsMathematicsSolutions on every page
1

Let p , q and r be three unequal numbers such that p , q and r are in AP. If (q-p) , (r-q) and p are in GP, then (p+q):(q+r):(r+p) equals

NDA 2026 Solution View → 2

If p^ th term of an AP is k , then what is the sum of p^ th term, (p+q)^ th term and (p-q)^ th term of the AP ?

NDA 2026 Solution View → 3

If p , g₁ , g₂ and q are in GP and m is the arithmetic mean of p and q , then g₁^2 g₂ + g₂^2 g₁ is equal to

NDA 2026 Solution View → 4

The sum of the first n terms of an AP is 3n^2+5n . If the m^ th term of the AP is 68 , then what is the value of m ?

NDA 2026 Solution View → 5

Passage: Let X(a,p) , Y(b,q) and Z(c,r) be the points such that a , b and c are in AP. Question: If p , q and r are not in AP and b=c , then the line joining the points X , Y and Z

NDA 2026 Solution View → 6

If (10 + ₁₀ x) , (10 + ₁₀ y) and (10 + ₁₀ z) are in AP, then consider the following statements: I. The GM of x and z is y^2 . II. The AM of ₁₀ x and ₁₀ z is ₁₀ y . Which of the sta

NDA 2025 Solution View → 7

How many terms of the series 1 + 3 + 5 + 7 + amount to a sum equal to 12345678987654321 ?

NDA 2025 Solution View → 8

For the following two (02) items: Let (6 + 10 + 14 + up to m terms ) = (1 + 3 + 5 + 7 + up to n terms ) , where m How many values of m are possible?

NDA 2025 Solution View → 9

For the following two (02) items: Let (6 + 10 + 14 + up to m terms ) = (1 + 3 + 5 + 7 + up to n terms ) , where m What is the relation between m and n ?

NDA 2025 Solution View → 10

How many terms are identical in the two APs 19, 21, 23, up to 110 terms and 19, 22, 25, 28, up to 75 terms?

NDA 2025 Solution View → 11

If p , 1 , q are in AP and p , 2 , q are in GP, then which of the following statements is/are correct? I. p , 4 , q are in HP. II. 1 p , 1 4 , 1 q are in AP. Select the answer usin

NDA 2025 Solution View → 12

The sum of the first 8 terms of a GP is five times the sum of its first 4 terms. If r 1 is the common ratio, then what is the number of possible real values of r ?

NDA 2025 Solution View → 13

If 5th, 7th and 13th terms of an AP are in GP, then what is the ratio of its first term to its common difference?

NDA 2025 Solution View → 14

The sum of the first k terms of a series S is 3k^2 + 5k . Which one of the following is correct?

NDA 2025 Solution View → 15

What is the harmonic mean of the numbers C(10, 3) , C(10, 4) , C(10, 5) , C(10, 6) and C(10, 7) ?

NDA 2025 Solution View → 16

If p times the p^ th term of an AP is equal to q times the q^ th term (p q) , then what is the (p+q)^ th term equal to?

NDA 2024 Solution View → 17

Let p= In (x), q= (x^3 ) and r = (x^5 ) , where x>1 . Which of the following statements is/are correct? A. p, q and r are in AP. B. p, q and r can never be in GP. Select the answer

NDA 2024 Solution View → 18

Paragraph: The product of 5 consecutive terms of an AP is 229635 . The first, second and fifth terms are in GP. Question: What is the sum of all five terms?

NDA 2024 Solution View → 19

If a, b, c are in AP ; b, c, d are in GP ; c, d , e are in HP, then which of the following is/are correct? 1. a, c and e are in GP 2. 1 a , 1 c , 1 e are in GP Select the correct a

NDA 2024 Solution View → 20

An edible oil is sold at the rates 150,200,250,300 rupees per litre in four consecutive years. Assuming that an equal amount of money is spent on oil by a family in every year duri

NDA 2024 Solution View → 21

Let m=77^n . The index n is given a positive integral value at random. What is the probability that the value of m will have 1 in the units place?

NDA 2024 Solution View → 22

array |c|c|c|c|c|c| x_i & 1 & 2 & 3 & & n f_i & 1 & 2⁻¹ & 2⁻² & & 2^ -(n-1) array What is _i^n x_i f_i equal to?

NDA 2024 Solution View → 23

Paragraph: The product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. Question: What is the common difference?

NDA 2024 Solution View → 24

If the sum of the first n terms of a series is n(2 n+1) , then what is the n th term?

NDA 2024 Solution View → 25

Let x>1, y>1, z>1 be in GP. Then 1 1+ x , 1 1+ y , 1 1+ z are

NDA 2024 Solution View → 26

The mean of n observations 1,4,9,16, , n^2 is 130 . What is the value of n ?

NDA 2024 Solution View → 27

If a, b, c are in HP, then what is 1 b-a + 1 b-c equal to? 1. 2 b 2. 1 a + 1 c 3. 1 2 ( 1 a + 1 b + 1 c ) Select the correct answer using the code given below:

NDA 2024 Solution View → 28

In an A P , the ratio of the sum of the first p terms to the sum of the first q terms is p^2: q^2 . Which one of the following is correct?

NDA 2024 Solution View → 29

If the n ^ th term of a sequence is 2 n+5 7 , then what is the sum of its first 140 terms?

NDA 2023 Solution View → 30

Let a₁, a₂, a₃ be in AP such that a₁+a₅+a₁₀+a₁₅+a₂₀+a₂₅+a₃₀+a₃₄=300 What is a₁+a₅-a₁₀-a₁₅-a₂₀-a₂₅+a₃₀+a₃₄ equal to?

NDA 2023 Solution View → 31

Let t₁, t₂, t₃, be in GP. What is (t₁ t₃ t₂₁ )^ 1 11 equal to?

NDA 2023 Solution View → 32

Let a₁, a₂, a₃ be in AP such that a₁+a₅+a₁₀+a₁₅+a₂₀+a₂₅+a₃₀+a₃₄=300 What is _ n=1 ³⁴ a_n equal to?

NDA 2023 Solution View → 33

What is the mean of the numbers 1,2,3, , 10 with frequencies ^9 c₀, ^9 c₁, ^9 c₂, , ^9 c₉ , respectively?

NDA 2023 Solution View → 34

If 2^ 1 c , 2^ b a c , 2^ 1 a are in GP, then which one of the following is correct?

NDA 2023 Solution View → 35

In an AP, the first term is x and the sum of the first n terms is zero. What is the sum of next m terms?

NDA 2023 Solution View → 36

p , q , r and s are in AP such that p + s =8 and qr =15 . What is the difference between largest and smallest numbers?

NDA 2023 Solution View → 37

The first and the second terms of an AP are 5 2 and 23 12 respectively. If n^ th terms is the largest negative term, what is the value of n ?

NDA 2023 Solution View → 38

Paragraph: Consider the sum S =0!+1!+2!+3!+4!+ +100! Question: If the sum S is divided by 60 , what is the remainder?

NDA 2023 Solution View → 39

Paragraph: Given that m( )= ^2 +n^2 ^2 +2 n , where n is a fixed positive real number. Question: What is the least value of m ( ) ?

NDA 2023 Solution View → 40

If G is the geometric mean of numbers 1,2,2^2, 2^3, , 2 n⁻¹ , then what is the value of 1+2 ₂ G ?

NDA 2023 Solution View → 41

If H is the harmonic mean of numbers 1,2.2^2, 2^3, , 2 n⁻¹ , then what is n / H equal to?

NDA 2023 Solution View → 42

If (a+b), 2 b,(b+c) are in HP, then which one of the following is correct?

NDA 2023 Solution View → 43

If H is the Harmonic Mean of three numbers ¹⁰ C ₄, ¹⁰ C ₅ , and ¹⁰ C ₆ , then what is the value of 270 H ?

NDA 2023 Solution View → 44

Paragraph: Let P be the sum of first n positive terms of an increasing arithmetic progression A . Let Q be the sum of first n positive terms of another increasing arithmetic progre

NDA 2022 Solution View → 45

Paragraph: Let P be the sum of first n positive terms of an increasing arithmetic progression A . Let Q be the sum of first n positive terms of another increasing arithmetic progre

NDA 2022 Solution View → 46

Paragraph: Let f(x) be a function satisfying f(x+y)=f(x) f(y) for all x, y N such that f(1)=2 : Question: If _ x=2 ^n f(x)=2044 , then what is the value of n ?

NDA 2022 Solution View → 47

Paragraph: Let f(x) be a function satisfying f(x+y)=f(x) f(y) for all x, y N such that f(1)=2 : Question: What is _ x=1 ^6 2^x f(x) equal to?

NDA 2022 Solution View → 48

Paragraph: Let P be the sum of first n positive terms of an increasing arithmetic progression A . Let Q be the sum of first n positive terms of another increasing arithmetic progre

NDA 2022 Solution View → 49

Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers. If x y = 55 42 , then what is the value of n ?

NDA 2022 Solution View → 50

If a+b 2 , b, b+c 2 are in HP, then which one of the following is correct?

NDA 2022 Solution View → 51

If the sum of the first 9 terms of an AP is equal to sum of the first 11 terms, then what is the sum of the first 20 terms?

NDA 2022 Solution View → 52

The marks obtained by 51 students in a class are in AP with its first term 4 and common difference 3 . What is the median of the marks?

NDA 2022 Solution View → 53

The marks obtained by 51 students in a class are in AP with its first term 4 and common difference 3 . What is the mean of the marks?

NDA 2022 Solution View → 54

If the 5th term of an AP is 1 10 and its 10 th term is 1 5 , then what is the sum of first 50 terms?

NDA 2022 Solution View → 55

What is the arithmetic mean of 50 terms of an AP with first term 4 and common difference 4 ?

NDA 2022 Solution View → 56

The marks obtained by 51 students in a class are in AP with its first term 4 and common difference 3 . What is the sum of the deviations measured from the median?

NDA 2022 Solution View → 57

If a, b, c are in GP where a 0, b 0, c 0 , then which of the following are correct? 1. a^2, b^2, c^2 are in GP 2. 1 a , 1 b , 1 c are in GP 3. a , b , c are in GP Select the correc

NDA 2022 Solution View → 58

What is the value of aligned & 2(2 1)+3(3 2 1)+4(4 3 2 1)+ & 5(5 4 3 2 1)+ + & 9(9 8 7 6 5 4 3 2 1)+2 ? aligned

NDA 2022 Solution View → 59

Let p, q and 3 be respectively the first, third and fifth terms of an A.P. Let d be the common difference. If the product (p q) is minimum, then what is the value of d ?

NDA 2021 Solution View → 60

If a_n=n(n!) , then what is a₁+a₂+a₃+ +a₁₀ equal to?

NDA 2021 Solution View → 61

If g is the geometric mean of 2,4,8,16,32,64,128,256,512 , 1024, then which one of the following is correct?

NDA 2021 Solution View → 62

If the harmonic mean of 60 and x is 48 , then what is the value of x ?

NDA 2021 Solution View → 63

If the first term of an AP is 2 and the sum of the first five terms is equal to one-fourth of the sum of the next five terms, then what is the sum of the first ten terms?

NDA 2021 Solution View → 64

Consider the following statements : 1. If each term of a GP is multiplied by same non-zero number, then the resulting sequence is also a GP. 2. If each term of a GP is divided by s

NDA 2021 Solution View → 65

If x^2, x,-8 are in AP, then which one of the following is correct?

NDA 2021 Solution View → 66

The third term of a GP is 3 . What is the product of its first five terms?

NDA 2021 Solution View → 67

Let x be the HM and y be the GM of two positive numbers m and n . If 5 x=4 y , then which one of the following is correct?

NDA 2021 Solution View → 68

The geometric mean of a set of observations is computed as 10 . The geometric mean obtained when each observation x_i is replaced by 3 x_i^4 is

NDA 2021 Solution View → 69

Let S_k denote the sum of first k terms of an AP. What is S₃₀ S₂₀-S₁₀ equal to?

NDA 2021 Solution View → 70

If p=(1111 up to n digits ) , then what is the value of 9 p^2+p ?

NDA 2021 Solution View → 71

If x, y, z are in GP, then which of the following is/are correct? 1. (3 x), (3 y), (3 z) are in AP 2. x y z+ (), x y z+ (y), x y z+ (z) are in HP Select the correct answer using th

NDA 2021 Solution View → 72

If 1 b+c , 1 c+a , 1 a+b are in HP, then Which of the following is/are correct? 1. a, b, c are in AP 2. (b+c)^2,(c+a)^2,(a+b)^2 are in GP Select the correct answer using the code g

NDA 2021 Solution View → 73

What is the mean of natural numbers contained in the interval [15,64] ?

NDA 2021 Solution View → 74

If p^2, q^2 and r^2 (where .p, q, r 0 ) are in GP, then which of the following is/are correct? 1. p, q and r are in GP. 2. p, q and r are in AP . Select the correct answer using th

NDA 2020 Solution View → 75

What is the value of 1-2+3-4+5- +101 ?

NDA 2019 Solution View → 76

If the sum of first n terms of a series is (n+12) , then what is its third term?

NDA 2019 Solution View → 77

A geometric progression (GP) consists of 200 terms. If the sum of odd terms of the GP is m , and the sum of even terms of the GP is n , then what is its common ratio?

NDA 2019 Solution View → 78

Let m and n(m n) be the roots of the equation x^2-16 x+39=0 . If four terms p, q, r and s are inserted between m and n to form an AP , then what is the value of p+q+r+s ?

NDA 2019 Solution View → 79

What is the value of 2+ 1 2+ 1 2+ 1 2+

NDA 2019 Solution View → 80

Let a, b, c be in AP and k 0 be a real number. Which of the following are correct? 1. k a, k b, k c are in AP 2. k-a, k-b, k-c are in AP 3. a k , b k , c k are in AP Select the cor

NDA 2019 Solution View → 81

Let S_n be the sum of the first n terms of an AP. If S_ 2 n =3 n+14 n^2 , then what is the common difference?

NDA 2019 Solution View → 82

If 3rd, 8th and 13th terms of a GP are p, q and r respectively, then which one of the following is correct?

NDA 2019 Solution View → 83

A car travels first 60 km at a speed of 3 v km / hr and travels next 60 km at 2 v km / hr . What is the average speed of the car?

NDA 2019 Solution View → 84

The numbers 1,5 and 25 can be three terms (not necessarily consecutive) of

NDA 2019 Solution View → 85

What is the n ^ th term of the sequence 25,-125,625 , -3125, ?

NDA 2019 Solution View → 86

What is the Fourth term of an AP of n terms whose sum is n ( n +1) ?

NDA 2019 Solution View → 87

The sum of (p+q)^ th and (p-q)^ th terms of an AP is equal to

NDA 2019 Solution View → 88

If an infinite GP has the first term x and the sum 5 , then which of the following is correct?

NDA 2018 Solution View → 89

The sum of the series 3-1+ 1 3 - 1 9 + . is equal to

NDA 2018 Solution View → 90

If u , vand w (all positive) are the p^ th , q^ th and r^ th terms of a GP, the determinant of the matrix | array lll In u & p & 1 In v & q & 1 In w & r & 1 array | is

NDA 2018 Solution View → 91

If x _ i 0, y _ i 0( i =1,2,3 n) are the values of two variable X and Y with geometric mean P and Q respectively, then the geometric mean of X Y is

NDA 2018 Solution View → 92

Let T_r be the r^ th term of an AP for r=1,2,3, If for some distinct positive integers m and n we have T _ m =1 / n and T _ n =1 / m , then what is T _ mn equal to?

NDA 2018 Solution View → 93

If the ratio of A M to G M of two positive numbers a and b is 5: 3 , then a : b is equal to

NDA 2018 Solution View → 94

What is the sum of all two-digit numbers which when divided by 3 leave 2 as the remainder?

NDA 2018 Solution View → 95

If x, 3 2 , z are in AP; x, 3, z are in GP; then which one of the following will be in HP?

NDA 2018 Solution View → 96

If the second term of a GP is 2 and the sum of its infinite term is 8 , then the GP is

NDA 2018 Solution View → 97

If a, b, c are in AP or GP HP, then a-b b-c is equal to

NDA 2018 Solution View → 98

The third term of a GP is 3 . What is the product of the first five terms?

NDA 2018 Solution View → 99

If x=1-y+y^2-y^3+ . up to infinite terms, where |y| 1 then which one of the following is correct?

NDA 2018 Solution View → 100

If S _ n = nP + n ( n -1) Q 2 , where S _ n denotes the sum of the first n terms of an AP , then the common difference is

NDA 2017 Solution View → 101

The value of the product 6^ 1 2 6^ 1 4 6^ 1 8 6^ 1 16 . up to infinite terms is

NDA 2017 Solution View → 102

If y=x+x^2+x^3+ up to infinite terms where x 1 , then which one of the following is correct?

NDA 2017 Solution View → 103

A person is to count 4500 notes. Let a_n denote the number of notes he counts in the nth minute. If a₁=a₂=a₃= . =a₁₀=150 , and a₁₀, a₁₁, a₁₂, . are in AP with the common difference

NDA 2017 Solution View → 104

The value of 1 ₃ e + 1 ₃ e^2 + 1 ₃ e^4 + . up to infinite terms is

NDA 2017 Solution View → 105

If 1.3+2.3^2+3.3^3+ .+ n .3^n= (2 n -1) 3^ a + b 3 then a and b are respectively

NDA 2017 Solution View → 106

What is the sum of the series 0.3+0.33+0.333+ . n terms?

NDA 2017 Solution View → 107

If the sum of m terms of an AP is n and the sum of n terms is m , then the sum of ( m + n ) terms is

NDA 2017 Solution View → 108

The fifth term of an AP of n terms, whose sum is n^2-2 n , is

NDA 2017 Solution View → 109

The sum of the first n terms of the series 1 2 + 3 4 + 7 8 + 15 16 + . is equal to

NDA 2017 Solution View → 110

Let f( n )= [ 1 4 + n 1000 ] , where [ x ] denote the integral part of x . Then the value of _ n=1 ¹⁰⁰⁰ f(n) is

NDA 2017 Solution View → 111

If x₁ and x₂ are positive quantities, then the condition for the difference between the arithmetic mean and the geometric mean to be greater than 1 is

NDA 2017 Solution View → 112

The sum of all the two-digit odd numbers is

NDA 2017 Solution View → 113

How many geometric progressions is/are possible containing 27,8 and 12 as three of its/their terms?

NDA 2016 Solution View → 114

Paragraph: Let a , x , y , z , b be in AP , where x + y + z =15 . Let a , p , q , r , b be in HP , where p ⁻¹+ q ⁻¹+ r ⁻¹= 5 3 Question: What is the value of x y z ?

NDA 2016 Solution View → 115

Paragraph: Let a , x , y , z , b be in AP , where x + y + z =15 . Let a , p , q , r , b be in HP , where p ⁻¹+ q ⁻¹+ r ⁻¹= 5 3 Question: What is the value of a b ?

NDA 2016 Solution View → 116

Paragraph: Let a , x , y , z , b be in AP , where x + y + z =15 . Let a , p , q , r , b be in HP , where p ⁻¹+ q ⁻¹+ r ⁻¹= 5 3 Question: What is the value of pqr?

NDA 2016 Solution View → 117

Paragraph: The sixth term of an AP is 2 and its common difference is greater than 1 . Question: What is the common difference of the AP so that the product of the first, fourth and

NDA 2016 Solution View → 118

Paragraph: The sixth term of an AP is 2 and its common difference is greater than 1 . Question: What is the first term of the AP so that the product of the first, fourth and fifth

NDA 2016 Solution View → 119

Paragraph: The interior angles of a polygon of n sides are in AP. The smallest angle is 120^ and the common difference is 5^ . Question: How many possible values can n have?

NDA 2016 Solution View → 120

What is the greatest value of the positive integer n satisfying the condition 1+ 1 2 + 1 4 + 1 8 + . .+ 1 2^ n -1 2- 1 1000 ?

NDA 2016 Solution View →
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