Sequences and Series PYQs - Last 10 Years

JEE Main / Mathematics / Algebra / 277 recent questions

MathematicsAlgebra2017-2026

All Sequences and Series PYQs Last 5 Years Create chapter test

Practice 277 JEE Main Mathematics questions from Sequences and Series. Use the year-wise and type-wise breakdown to prioritize recent PYQs, then continue into the question list below.

277

PYQs on Page

Mathematics / Algebra

2017-2026

Year Range

Based on indexed question metadata

170

Last 5 Years

2022-2026

277

Last 10 Years

2017-2026

Recent Year Trend

2021

2022

2023

2024

2025

2026

202139 max PYQs/year2026

Question Types

277PYQs

MCQ70.8%

INTEGER29.2%

Difficulty Mix

#1 Medium234

#2 Easy24

#3 Hard19

170 in last 5 years277 in last 10 years

Last 10 Years Sequences and Series Questions

Showing 27 of 277 filtered questions.

1Sequences And Series

For x \(\varepsilon\) R, let [x] denote the greatest integer \(\le\) x, then the sum of the series
$$\left[ { - {1 \over 3}} \right] + \left[ { - {1 \over 3} - {1 \over {100}}} \right] + \left[ { - {1 \over 3} - {2 \over {100}}} \right] ...

2Sequences And Series

Let Sn denote the sum of the first n terms of an A.P. If S4 = 16 and S6= – 48, then S10 is equal to :

3Sequences And Series

If a1, a2, a3, ..... are in A.P. such that a1 + a7 + a16 = 40, then the sum of the first 15 terms of this A.P. is :

4Sequences And Series

The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is \({{27} \over {19}}\).Then the common ratio of this series is :

5Sequences And Series

Let a1, a2, . . . . . ., a10 be a G.P. If \({{{a_3}} \over {{a_1}}} = 25,\) then \({{{a_9}} \over {{a_5}}}\) equals

6Sequences And Series

If 19th term of a non-zero A.P. is zero, then its (49th term) : (29th term) is :

7Sequences And Series

Let x, y be positive real numbers and m, n positive integers. The maximum value of the expression \({{{x^m}{y^n}} \over {\left( {1 + {x^{2m}}} \right)\left( {1 + {y^{2n}}} \right)}}\) is :

8Sequences And Series

The sum of all two digit positive numbers which when divided by 7 yield 2 or 5 as remainder is -

9Sequences And Series

Let a1, a2, a3, ..... a10 be in G.P. with ai > 0 for i = 1, 2, ….., 10 and S be the set of pairs (r, k), r, k \(\in\) N (the set of natural numbers) for which
$$\left| {\matrix{
{{{\log }_e}\,{a_1}^r{a_2}^k} & {{{\log }_e}\,{a_2}^r{a_3...

10Sequences And Series

If a1, a2, a3, ............... an are in A.P. and a1 + a4 + a7 + ........... + a16 = 114, then a1 + a6 + a11 + a16 is equal to :

11Sequences And Series

The sum
\({{3 \times {1^3}} \over {{1^3}}} + {{5 \times ({1^3} + {2^3})} \over {{1^2} + {2^2}}} + {{7 \times \left( {{1^3} + {2^3} + {3^3}} \right)} \over {{1^2} + {2^2} + {3^2}}} + .....\) upto 10 terms is:

12Sequences And Series

Let a1, a2, a3,......be an A.P. with a6 = 2. Then the common difference of this A.P., which maximises the
product a1a4a5, is :

13Sequences And Series

Let \(a\), b and c be in G.P. with common ratio r, where \(a\) \(\ne\) 0 and 0 < r \(\le\) \({1 \over 2}\)
. If 3\(a\), 7b and 15c are the first three
terms of an A.P., then the 4th term of this A.P. is :

14Sequences And Series

The sum
\(1 + {{{1^3} + {2^3}} \over {1 + 2}} + {{{1^3} + {2^3} + {3^3}} \over {1 + 2 + 3}} + ...... + {{{1^3} + {2^3} + {3^3} + ... + {{15}^3}} \over {1 + 2 + 3 + ... + 15}}\)\(- {1 \over 2}\left( {1 + 2 + 3 + ... + 15} \right)\) is equal...

15Sequences And Series

The sum of the first 20 terms of the series
\(1 + {3 \over 2} + {7 \over 4} + {{15} \over 8} + {{31} \over {16}} + ...,\) is :

16Sequences And Series

Let \({1 \over {{x_1}}},{1 \over {{x_2}}},...,{1 \over {{x_n}}}\,\,\) (xi \(\ne\) 0 for i = 1, 2, ..., n) be in A.P. such that x1=4 and x21 = 20. If n is the least positive integer for which \({x_n} > 50,\) then $$\sum\limits_{i = 1}^n {\...

17Sequences And Series

If x1, x2, . . ., xn and \({1 \over {{h_1}}}\), \({1 \over {{h_2}}}\), . . . , \({1 \over {{h_n}}}\) are two A.P..s such that x3 = h2 = 8 and x8 = h7 = 20, then x5.h10 equals :

18Sequences And Series

If b is the first term of an infinite G.P. whose sum is five, then b lies in the interval :

19Sequences And Series

Let An = \(\left( {{3 \over 4}} \right) - {\left( {{3 \over 4}} \right)^2} + {\left( {{3 \over 4}} \right)^3}\) \(-\). . . . . + (\(-\)1)n-1 \({\left( {{3 \over 4}} \right)^n}\) and Bn = 1 \(-\) An.
Then, the least dd natural numb...

20Sequences And Series

If a, b, c are in A.P. and a2, b2, c2 are in G.P. such that
a < b < c and a + b + c = \({3 \over 4},\) then the value of a is :

21Sequences And Series

Let A be the sum of the first 20 terms and B be the sum of the first 40 terms of the series
12 + 2.22 + 32 + 2.42 + 52 + 2.62 ...........
If B - 2A = 100\(\lambda\), then \(\lambda\) is equal to

22Sequences And Series

Let \({a_1}\), \({a_2}\), \({a_3}\), ......... ,\({a_{49}}\) be in A.P. such that
\(\sum\limits_{k = 0}^{12} {{a_{4k + 1}}} = 416\) and \({a_9} + {a_{43}} = 66\).
\(a_1^2 + a_2^2 + ....... + a_{17}^2 = 140m\), then m is equal to

23Sequences And Series

Let
Sn = \({1 \over {{1^3}}}\)\(+ {{1 + 2} \over {{1^3} + {2^3}}} + {{1 + 2 + 3} \over {{1^3} + {2^3} + {3^3}}} + ......... + {{1 + 2 + ....... + n} \over {{1^3} + {2^3} + ...... + {n^3}}}.\)
If 100 Sn = n, then n is equal to :

24Sequences And Series

If three positive numbers a, b and c are in A.P. such that abc = 8, then the minimum possible value of b is :

25Sequences And Series

If the arithmetic mean of two numbers a and b, a > b > 0, is five times their geometric mean, then \({{a + b} \over {a - b}}\) is equal to :

26Sequences And Series

If the sum of the first n terms of the series \(\,\sqrt 3 + \sqrt {75} + \sqrt {243} + \sqrt {507} + ......\) is \(435\sqrt 3 ,\) then n equals :

27Sequences And Series

For any three positive real numbers a, b and c,
9(25\({a^2}\) + b2) + 25(c2 - 3\(a\)c) = 15b(3\(a\) + c).
Then