JEE Main 2024 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 4 April 2024, Shift 1, Maths Q9

Question 9 of 90 in this shift, Maths question 9 of 30, Section A.

Let the first three terms

2

p

and

q

, with

q \neq 2

, of a G.P. be respectively the

7^{th}

8^{th}

and

13^{th}

terms of an A.P. If the

5^{th}

term of the G.P. is the

n^{th}

term of the A.P., then n is equal to :

(1) $151$
(2) $163$ Official answer
(3) $169$
(4) $177$

Official answer

Option 2

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: GP General Term

Same idea in other shifts

Asked 15× in all

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
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
8 Apr 2024, Shift 2 · Q8In an increasing geometric progression of positive terms, the sum of the second and sixth terms is $\frac{70}{3}$ and the product of the…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
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
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
26 Jun 2022, Shift 2 · Q27If $a_1\ (> 0), a_2, a_3, a_4, a_5$ are in a G.P., $a_2 + a_4 = 2a_3 + 1$ and $3a_2 + a_3 = 2a_4$ , then $a_2 + a_4 + 2a_5$ is equal to…MediumNumerical value
28 Jun 2022, Shift 1 · Q6Let $A_1, A_2, A_3, ....$ be an increasing geometric progression of positive real numbers. If $A_1A_3A_5A_7=\frac{1}{1296}$ and…MediumSingle correct

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 108 of the 174 JEE Main shifts held from 2017 to 2026.