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 50 of 277 filtered questions.

1Sequences And Series

Let Sn = 1 . (n \(-\) 1) + 2 . (n \(-\) 2) + 3 . (n \(-\) 3) + ..... + (n \(-\) 1) . 1, n \(\ge\) 4.The sum \(\sum\limits_{n = 4}^\infty {\left( {{{2{S_n}} \over {n!}} - {1 \over {(n - 2)!}}} \right)}\) is equal to :

2Sequences And Series

If \(\alpha\), \(\beta\) are natural numbers such that 100\(\alpha\) \(-\) 199\(\beta\) = (100)(100) + (99)(101) + (98)(102) + ...... + (1)(199), then the slope of the line passing through (\(\alpha\), \(\beta\)) and origin is :

3Sequences And Series

\({1 \over {{3^2} - 1}} + {1 \over {{5^2} - 1}} + {1 \over {{7^2} - 1}} + .... + {1 \over {{{(201)}^2} - 1}}\) is equal to

4Sequences And Series

Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 \(-\) S1) is 1000, then the sum of the first 6n terms of the arithmetic progression is equal to...

5Sequences And Series

Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these ...

INTEGER+4 / -12021

6Sequences And Series

Sn(x) = loga1/2x + loga1/3x + loga1/6x + loga1/11x + loga1/18x + loga1/27x + ...... up to n-terms, where a > 1. If S24(x) = 1093 and S12(2x) = 265, then value of a is equal to ____________.

INTEGER+4 / -12021

7Sequences And Series

Let \({1 \over {16}}\), a and b be in G.P. and \({1 \over a}\), \({1 \over b}\), 6 be in A.P., where a, b > 0. Then 72(a + b) is equal to ___________.

INTEGER+4 / -12021

8Sequences And Series

The product \({2^{{1 \over 4}}}{.4^{{1 \over {16}}}}{.8^{{1 \over {48}}}}{.16^{{1 \over {128}}}}\) ... to \(\infty\) is equal
to :

9Sequences And Series

The number of terms common to the two A.P.'s
3, 7, 11, ....., 407 and 2, 9, 16, ....., 709 is ______.

INTEGER+4 / -02020

10Sequences And Series

Let an be the nth term of a G.P. of positive terms.
\(\sum\limits_{n = 1}^{100} {{a_{2n + 1}} = 200}\) and \(\sum\limits_{n = 1}^{100} {{a_{2n}} = 100}\),

then \(\sum\limits_{n = 1}^{200} {{a_n}}\) is equal to :

11Sequences And Series

The sum \(\sum\limits_{k = 1}^{20} {\left( {1 + 2 + 3 + ... + k} \right)}\) is :

INTEGER+4 / -02020

12Sequences And Series

Let ƒ : R \(\to\) R be such that for all
x \(\in\) R (21+x + 21–x), ƒ(x) and (3x + 3–x) are in
A.P., then the minimum value of ƒ(x) is

13Sequences And Series

If the 10th term of an A.P. is \({1 \over {20}}\) and its 20th term
is \({1 \over {10}}\), then the sum of its first 200 terms is

14Sequences And Series

The sum, \(\sum\limits_{n = 1}^7 {{{n\left( {n + 1} \right)\left( {2n + 1} \right)} \over 4}}\) is equal to
________.

INTEGER+4 / -02020

15Sequences And Series

Five numbers are in A.P. whose sum is 25 and product is 2520. If one of these five numbers is -\({1 \over 2}\) , then the greatest number amongst them is:

16Sequences And Series

If the sum of the first 40 terms of the series, 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 + ..... is (102)m, then m is equal to :

17Sequences And Series

Let \({a_1}\)
, \({a_2}\)
, \({a_3}\)
,....... be a G.P. such that \({a_1}\)
< 0, \({a_1}\)
+ \({a_2}\)
= 4 and \({a_3}\)
+ \({a_4}\)
= 16. If \(\sum\limits_{i = 1}^9 {{a_i}} = 4\lambda\), then \(\lambda\) is
equal to:

18Sequences And Series

Let a , b, c , d and p be any non zero distinct real numbers such that
(a2 + b2 + c2)p2 – 2(ab + bc + cd)p + (b2 + c2 + d2) = 0. Then :

19Sequences And Series

The common difference of the A.P. b1, b2, … , bm
is 2 more than the common difference of A.P. a1, a2, …, an. If a40 = –159, a100 = –399 and
b100 = a70, then b1
is equal to :

20Sequences And Series

If \({3^{2\sin 2\alpha - 1}}\), 14 and \({3^{4 - 2\sin 2\alpha }}\) are the first three terms of an A.P. for some \(\alpha\), then the sixth
terms of this A.P. is:

21Sequences And Series

If 210 + 29.31 + 28
.32 +.....+ 2.39 + 310 = S - 211, then S is equal to :

22Sequences And Series

If the sum of the second, third and fourth terms
of a positive term G.P. is 3 and the sum of its
sixth, seventh and eighth terms is 243, then the
sum of the first 50 terms of this G.P. is :

23Sequences And Series

If the sum of the first 20 terms of the series
\({\log _{\left( {{7^{1/2}}} \right)}}x + {\log _{\left( {{7^{1/3}}} \right)}}x + {\log _{\left( {{7^{1/4}}} \right)}}x + ...\) is 460,
then x is equal to :

24Sequences And Series

If 1+(1–22.1)+(1–42.3)+(1-62.5)+......+(1-202.19)= \(\alpha\) - 220\(\beta\), then an ordered pair \(\left( {\alpha ,\beta } \right)\) is equal to:

25Sequences And Series

The minimum value of 2sinx + 2cosx is :

26Sequences And Series

Let a1, a2, ..., an be a given A.P. whose common difference is an integer and Sn = a1 + a2 + .... + an. If a1 = 1, an = 300 and 15 \(\le\) n \(\le\) 50, then the ordered pair (Sn-4, an–4) is equal to:

27Sequences And Series

If the first term of an A.P. is 3 and the sum of
its first 25 terms is equal to the sum of its next
15 terms, then the common difference of this
A.P. is :

28Sequences And Series

The value of \({\left( {0.16} \right)^{{{\log }_{2.5}}\left( {{1 \over 3} + {1 \over {{3^2}}} + ....to\,\infty } \right)}}\) is equal to ______.

INTEGER+4 / -02020

29Sequences And Series

If the sum of the series
20 + 19\({3 \over 5}\) + 19\({1 \over 5}\) + 18\({4 \over 5}\) + ...
upto nth term is 488
and the nth term is negative, then :

30Sequences And Series

If m arithmetic means (A.Ms) and three
geometric means (G.Ms) are inserted between
3 and 243 such that 4th A.M. is equal to 2nd
G.M., then m is equal to _________ .

INTEGER+4 / -02020

31Sequences And Series

If |x| < 1, |y| < 1 and x \(\ne\) y, then the sum to infinity
of the following series
(x + y) + (x2+xy+y2) + (x3+x2y + xy2+y3) + ....

32Sequences And Series

The sum of the first three terms of a G.P. is S and
their product is 27. Then all such S lie in :

33Sequences And Series

Let S be the sum of the first 9 terms of the
series :
{x + k\(a\)} + {x2 + (k + 2)\(a\)} + {x3 + (k + 4)\(a\)}
+ {x4 + (k + 6)\(a\)} + .... where a \(\ne\) 0 and x \(\ne\) 1.
If S = $${{{x^{10}} - x + 45a\left( {x - 1} \right)} \over {...

34Sequences And Series

If the sum of first 11 terms of an A.P.,
a1, a2, a3, ....
is 0 (a \(\ne\) 0), then the sum of the A.P.,
a1
, a3
, a5
,....., a23 is ka1
, where k is equal to :

35Sequences And Series

If a, b, c be three distinct real numbers in G.P. and a + b + c = xb , then x cannot be

36Sequences And Series

Let \({a_1},{a_2},.......,{a_{30}}\) be an A.P.,
\(S = \sum\limits_{i = 1}^{30} {{a_i}}\) and \(T = \sum\limits_{i = 1}^{15} {{a_{\left( {2i - 1} \right)}}}\).
If \(a_5\) = 27 and S - 2T = 75, then \(a_{10}\) is equal to :

37Sequences And Series

The sum of the following series
\(1 + 6 + {{9\left( {{1^2} + {2^2} + {3^2}} \right)} \over 7} + {{12\left( {{1^2} + {2^2} + {3^2} + {4^2}} \right)} \over 9}\)
$$ + {{15\left( {{1^2} + {2^2} + ... + {5^2}} \right)} \over {11}} + ........

38Sequences And Series

Let a, b and c be the 7th, 11th and 13th terms respectively of a non-constant A.P. If these are also three consecutive terms of a G.P., then \({a \over c}\) equal to :

39Sequences And Series

Let the sum of the first n terms of a non-constant
A.P., a1, a2, a3, ..... be \(50n + {{n(n - 7)} \over 2}A\), where
A is a constant. If d is the common difference of
this A.P., then the ordered pair (d, a50) is equal to

40Sequences And Series

If the sum and product of the first three term in
an A.P. are 33 and 1155, respectively, then a value
of its 11th term is :-

41Sequences And Series

Some identical balls are arranged in rows to form
an equilateral triangle. The first row consists of one
ball, the second row consists of two balls and so
on. If 99 more identical balls are addded to the total
number of balls used in formin...

42Sequences And Series

The sum of the series 1 + 2 × 3 + 3 × 5 + 4 × 7 +....
upto 11th term is :-

43Sequences And Series

The sum of all natural numbers 'n' such that
100 < n < 200 and H.C.F. (91, n) > 1 is :

44Sequences And Series

If three distinct numbers a, b, c are in G.P. and the
equations ax2
+ 2bx + c = 0 and
dx2
+ 2ex + ƒ = 0 have a common root, then
which one of the following statements is
correct?

45Sequences And Series

The sum
\(\sum\limits_{k = 1}^{20} {k{1 \over {{2^k}}}}\) is equal to

46Sequences And Series

Let Sk = \({{1 + 2 + 3 + .... + k} \over k}.\) If \(S_1^2 + S_2^2 + .....\, + S_{10}^2 = {5 \over {12}}\)A, then A is equal to :

47Sequences And Series

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :

48Sequences And Series

If nC4, nC5 and nC6 are in A.P., then n can be :

49Sequences And Series

If sin4\(\alpha\) + 4 cos4\(\beta\) + 2 = 4\(\sqrt 2\) sin \(\alpha\) cos \(\beta\); \(\alpha\), \(\beta\) \(\in\) [0, \(\pi\)],
then cos(\(\alpha\) + \(\beta\)) \(-\) cos(\(\alpha\) \(-\) \(\beta\)) is equal to :

50Sequences And Series

If the sum of the first 15 terms of the series \({\left( {{3 \over 4}} \right)^3} + {\left( {1{1 \over 2}} \right)^3} + {\left( {2{1 \over 4}} \right)^3} + {3^3} + {\left( {3{3 \over 4}} \right)^3} + ....\) is equal to 225 k, then k
is equa...