JEE Main 2026 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 6 April 2026, Shift 1, Maths Q6

Question 6 of 75 in this shift, Maths question 6 of 25, Section A.

The 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 to the common ratio of the G.P. and the first term of the G.P. is equal to common difference of the A.P., then the sum of all possible values of the first term of the G.P. is:

(1) $\frac{34}{9}$ Official answer
(2) $\frac{34}{13}$
(3) $\frac{32}{9}$
(4) $\frac{32}{13}$

Official answer

Option 1

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: AP Sum of n terms

Same idea in other shifts

Asked 15× in all

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
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

Question text from the official JEE Main paper published by NTA; answer from the final answer key. Chapter, topic and idea tags, difficulty and skill are Lumi’s. Lumi analyses 42 of the 174 JEE Main shifts held from 2017 to 2026.