JEE Main Maths · Sequences and Series

AP and GP in JEE Main

Name: AP and GP: JEE Main previous year questions
Creator: Lumi

AP and GP (Maths, Sequences and Series) came 59 times in 37 of the 42 JEE Main shifts Lumi analysed, across 17 distinct ideas. 35 of them came in 2024–26; it was last asked in 2026.

Questions: 59; in 37 shifts
Ideas asked: 17; 9 asked more than once
Numerical answer: 16; 27% of its questions
Pattern: Asked most years; last asked 2026

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 10Medium 41Hard 8

Format

Single correct43 Q
Numerical value16 Q

Ideas inside the topic

17 ideas

AP Sum of n terms15 Q
Method of Differences for Telescoping Series8 Q
GP General Term6 Q
GP Sum of n terms5 Q
Infinite GP Sum5 Q
AP General Term4 Q
Method of Differences (Vn Method)4 Q
Conditions for Three Terms in AP or GP2 Q
Counting Common Terms of Finite APs2 Q
Symmetric Selection of AP Terms1 Q
AP Recognition from Quadratic Sum1 Q
GP Sum of Squares1 Q

Where it sits

Part of Sequences and Series, which had 73 questions in all. AP and GP accounts for 81% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Some questions sit in other chapters too: Probability, Relations and Functions, Statistics.

Every question

All 59 AP and GP questions

Newest first, each with its options and official answer.

2 Apr 2026, Shift 1 · Q5Let $A$ 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…MediumSingle correct
2 Apr 2026, Shift 2 · Q4Let $a_1, a_2, a_3, \ldots$ be an A.P. and $g_1, g_2, g_3, \ldots$ be an increasing G.P. If $a_1 = a_2 + g_2 = 1$ and $a_3 + g_3 = 4$ ,…MediumSingle correct
2 Apr 2026, Shift 2 · Q5The sum $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \ldots$ up to 8 terms, is:MediumSingle correct
4 Apr 2026, Shift 1 · Q7The first term of an A.P. of $30$ non-negative terms is $\frac{10}{3}$ . If the sum of this A.P. is the cube of its last term, then its…MediumSingle correct
4 Apr 2026, Shift 2 · Q7Let $\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty$ and $\beta=\frac13+\frac19+\frac1{27}+\ldots\infty$ . Then the value of…EasySingle correct
5 Apr 2026, Shift 1 · Q2Let 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:EasySingle correct
5 Apr 2026, Shift 1 · Q5 $\sum_{n=1}^{10}\left(\frac{528}{n(n+1)(n+2)}\right)$ is equal to:EasySingle correct
5 Apr 2026, Shift 2 · Q5If the sum of the first 10 terms of the series…HardSingle correct
5 Apr 2026, Shift 2 · Q6Let $A_1, A_2, A_3, \dots\dots, A_{39}$ be 39 arithmetic means between the numbers 59 and 159. Then the mean of $A_{25}, A_{28}, A_{31}$ …EasySingle correct
6 Apr 2026, Shift 1 · Q6The 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…MediumSingle correct
6 Apr 2026, Shift 1 · Q24For the functions $f(\theta)=\alpha\tan^2\theta+\beta\cot^2\theta$ , and $g(\theta)=\alpha\sin^2\theta+\beta\cos^2\theta$ ,…HardNumerical value
8 Apr 2026, Shift 2 · Q5Let $\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \ldots$ up to 40 terms. If $(\tan\beta)^{\frac{\alpha}{1020}}$ is a root of the equation…MediumSingle correct
2 Apr 2025, Shift 1 · Q19Let $a_1, a_2, a_3,\ldots$ be in an A.P. such that $\sum_{k=1}^{12}a_{2k-1}=-\frac{72}{5}a_1$ , $a_1\neq0$ . If $\sum_{k=1}^{n}a_k=0$ , then…MediumSingle correct
2 Apr 2025, Shift 2 · Q5The 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…MediumSingle correct
2 Apr 2025, Shift 2 · Q22If the sum of the first 10 terms of the series…HardNumerical value
3 Apr 2025, Shift 1 · Q6Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive numbers. If $a_3 a_5 = 729$ and $a_2 + a_4 = \frac{111}{4}$ , then…EasySingle correct
3 Apr 2025, Shift 1 · Q7The sum $1 + 3 + 11 + 25 + 45 + 71 + \ldots$ upto 20 terms, is equal toMediumSingle correct
3 Apr 2025, Shift 1 · Q22All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the…HardNumerical value
4 Apr 2025, Shift 2 · Q5If the sum of the first 20 terms of the series…MediumSingle correct
4 Apr 2025, Shift 2 · Q6Consider 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…MediumSingle correct
7 Apr 2025, Shift 1 · Q6Let $x_1, x_2, x_3, x_4$ be in a geometric progression. If $2, 7, 9, 5$ are subtracted respectively from $x_1, x_2, x_3, x_4$ , then the…MediumSingle correct
7 Apr 2025, Shift 2 · Q6Let $a_n$ be the $n^{\mathrm{th}}$ term of an A.P. If $S_n=a_1+a_2+a_3+\ldots+a_n=700$ , $a_6=7$ and $S_7=7$ , then $a_n$ is equal to :MediumSingle correct
7 Apr 2025, Shift 2 · Q7If 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…MediumSingle correct
6 Apr 2024, Shift 2 · Q7A software company sets up $m$ number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start…MediumSingle correct
6 Apr 2024, Shift 2 · Q16Let $ABC$ be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle $ABC$ and the…MediumSingle correct
8 Apr 2024, Shift 1 · Q25Let the positive integers be written in the form : 1 2 3 4 5 6 7 8 9 10 ... If the $k^{\mathrm{th}}$ row contains exactly $k$ numbers for…MediumNumerical valueHas a figure
9 Apr 2024, Shift 1 · Q5If the sum of the series $\frac{1}{1\cdot(1+d)}+\frac{1}{(1+d)(1+2d)}+\ldots+\frac{1}{(1+9d)(1+10d)}$ is equal to $5$ , then $50d$ is equal…MediumSingle correct
9 Apr 2024, Shift 1 · Q26If a function $f$ satisfies $f(m+n)=f(m)+f(n)$ for all $m,n\in\mathbf{N}$ and $f(1)=1$ , then the largest natural number $\lambda$ such…MediumNumerical value
9 Apr 2024, Shift 2 · Q7Let $a, ar, ar^2, \ldots$ be an infinite G.P. If $\sum_{n=0}^{\infty}ar^n=57$ and $\sum_{n=0}^{\infty}a^3r^{3n}=9747$ , then $a+18r$ is…MediumSingle correct
9 Apr 2024, Shift 2 · Q24If…HardNumerical value
29 Jan 2024, Shift 1 · Q7If 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…MediumSingle correct
30 Jan 2024, Shift 2 · Q6Let $a$ and $b$ be be two distinct positive real numbers. Let $11^{\mathrm{th}}$ term of a GP, whose first term is $a$ and third term is…EasySingle correct
30 Jan 2024, Shift 2 · Q25Let $S_n$ be the sum to $n$ -terms of an arithmetic progression $3, 7, 11, \ldots$ . If…MediumNumerical value
31 Jan 2024, Shift 1 · Q5The sum of the series $\frac{1}{1-3\cdot1^2+1^4}+\frac{2}{1-3\cdot2^2+2^4}+\frac{3}{1-3\cdot3^2+3^4}+\ldots$ up to 10-terms isMediumSingle correct
31 Jan 2024, Shift 2 · Q7Let $2^{nd}$ , $8^{th}$ and $44^{th}$ terms of a non-constant A. P. be respectively the $1^{st}$ , $2^{nd}$ and $3^{rd}$ terms of a G. P. If…MediumSingle correct
6 Apr 2023, Shift 1 · Q7The sum of the first 20 terms of the series $5+11+19+29+41+\ldots$ isMediumSingle correct
6 Apr 2023, Shift 1 · Q8Let $a_1,a_2,a_3,\ldots,a_n$ be $n$ positive consecutive terms of an arithmetic progression. If $d>0$ is its common difference, then…MediumSingle correct
8 Apr 2023, Shift 2 · Q8Let $a_n$ be the $n^{th}$ term of the series $5 + 8 + 14 + 23 + 35 + 50 + \ldots$ and $S_n = \sum_{k=1}^{n} a_k$ . Then $S_{30} - a_{40}$ …MediumSingle correct
8 Apr 2023, Shift 2 · Q24Let $0 < z < y < x$ be three real numbers such that $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in an arithmetic progression and…HardNumerical value
13 Apr 2023, Shift 2 · Q8Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive numbers. Let the sum of its $6^{th}$ and $8^{th}$ terms be $2$ and the…MediumSingle correct
25 Jul 2022, Shift 1 · Q24Let $a,\ b$ be two non-zero real numbers. If $p$ and $r$ are the roots of the equation $x^2-8ax+2a=0$ and $q$ and $s$ are the roots of the…HardNumerical value
25 Jul 2022, Shift 1 · Q25Let $a_1=b_1=1$ , $a_n=a_{n-1}+2$ and $b_n=a_n+b_{n-1}$ for every natural number $n\ge2$ . Then $\sum_{n=1}^{15}a_n\cdot b_n$ is equal to…MediumNumerical value
28 Jul 2022, Shift 1 · Q28Let $x_1,x_2,x_3,\ldots,x_{20}$ be in geometric progression with $x_1=3$ and the common ratio $\frac{1}{2}$ . A new data is constructed…MediumNumerical value
24 Jun 2022, Shift 1 · Q13If $\{a_i\}_{i=1}^{n}$ , where n is an even integer, is an arithmetic progression with common difference 1, and $\sum_{i=1}^{n} a_i = 192$ ,…MediumSingle correct
3 Aug 2021, Shift 2 · Q67If ' $m$ ' is the arithmetic mean of two distinct real numbers $l$ and $n$ $(l, n > 1)$ and $G_1$ , $G_2$ and $G_3$ are three geometric means…MediumSingle correct
3 Aug 2021, Shift 2 · Q83If the sum of all 3-digit numbers which are multiples of 9 is $41k$ , then ' $k$ ' is equal to $\underline{\hspace{2em}}$ .EasyNumerical value
25 Jul 2021, Shift 1 · Q76Let $S_n$ be the sum of the first n terms of an arithmetic progression. If $S_{3n}=3S_{2n}$ , then the value of $\frac{S_{4n}}{S_{2n}}$ is :EasySingle correct
16 Mar 2021, Shift 2 · Q89Let $\frac{1}{16}$ , a and b be in G.P. and $\frac1a,\frac1b$ , 6 be in A.P., where $a,b>0$ . Then $72(a+b)$ is equal to ________.MediumNumerical value
18 Mar 2021, Shift 1 · Q68 $\frac{1}{3^2-1}+\frac{1}{5^2-1}+\frac{1}{7^2-1}+\ldots+\frac{1}{(201)^2-1}$ is equal to :MediumSingle correct
8 Jan 2020, Shift 1 · Q56Let $f:\mathbf{R}\to\mathbf{R}$ be such that for all $x\in\mathbf{R}$ , $(2^{1+x}+2^{1-x})$ , $f(x)$ and $(3^x+3^{-x})$ are in A.P., then…MediumSingle correct
8 Jan 2020, Shift 1 · Q73The sum $\displaystyle\sum_{k=1}^{20}(1+2+3+\ldots+k)$ is ______.EasyNumerical value
9 Jan 2020, Shift 2 · Q57Let $a_n$ be the $n^{\mathrm{th}}$ term of a G.P. of positive terms. If $\sum_{n=1}^{100}a_{2n+1}=200$ and $\sum_{n=1}^{100}a_{2n}=100$ ,…MediumSingle correct
9 Jan 2020, Shift 2 · Q69If $x=\sum_{n=0}^{\infty}(-1)^n\tan^{2n}\theta$ and $y=\sum_{n=0}^{\infty}\cos^{2n}\theta$ , for $0<\theta<\frac{\pi}{4}$ , then :EasySingle correct
9 Jan 2020, Shift 2 · Q72The number of terms common to the two A.P.'s $3,7,11,\ldots,407$ and $2,9,16,\ldots,709$ is ______.MediumNumerical value
2 Sep 2020, Shift 1 · Q57The sum of the first three terms of a G.P. is $S$ and their product is 27. Then all such $S$ lie in :MediumSingle correct
2 Sep 2020, Shift 1 · Q58If $|x|<1$ , $|y|<1$ and $x\neq y$ , then the sum to infinity of the following series…MediumSingle correct
6 Sep 2020, Shift 2 · Q56The common difference of the A.P. $b_1, b_2, \ldots, b_m$ is 2 more than the common difference of A.P. $a_1, a_2, \ldots, a_n$ . If…MediumSingle correct
6 Sep 2020, Shift 2 · Q73Suppose that a function $f:\mathbf{R}\to\mathbf{R}$ satisfies $f(x+y)=f(x)f(y)$ for all $x,y\in\mathbf{R}$ and $f(1)=3$ . If…MediumNumerical value
2 Apr 2017 (offline) · Q68For any three positive real numbers a, b and c, $9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c)$ . Then :HardSingle correct