JEE Main Maths · Sequences and Series

AP Sum of n terms

AP Sum of n terms (Sequences and Series) was asked 15 times in 15 JEE Main shifts, 2020–2026, out of the 42 shifts Lumi analysed. 6 of the 15 had a numerical answer.

Times asked: 15; in 15 shifts
Years: 2020–2026
Usual format: Single correct; Multi-step
Pattern: Asked most years; repeats across shifts

How it is asked

Sum of series with summation general term
Find common difference from ap sum condition

Difficulty

Easy 3Medium 12Hard 0

Where it sits

Chapter: Sequences and Series. Topic: AP and GP, 59 questions over 17 ideas.

All 15 questions

Newest first, each with its options and official answer.

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
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
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
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
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
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 · 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
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
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
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 · 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
8 Jan 2020, Shift 1 · Q73The sum $\displaystyle\sum_{k=1}^{20}(1+2+3+\ldots+k)$ is ______.EasyNumerical value