JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 July 2022, Shift 2, Maths Q7

Question 7 of 90 in this shift, Maths question 7 of 30, Section A.

Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be

\frac{98}{25}

. Then the sum of the first 21 terms of an AP, whose first term is 10ar,

n^{th}

term is

a_n

and the common difference is

10ar^2

, is equal to :

(1) $21\ a_{11}$ Official answer
(2) $22\ a_{11}$
(3) $15\ a_{16}$
(4) $14\ a_{16}$

Official answer

Option 1

NTA final key.

Chapter: Sequences and Series
Topic: AP and GP
Idea tested: Infinite GP Sum

Same idea in other shifts

Asked 15× in all

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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
15 Apr 2023, Shift 1 · Q24If the sum of the series…HardNumerical value
26 Jun 2022, Shift 2 · Q3If $A = \sum_{n=1}^{\infty} \frac{1}{(3 + (-1)^n)^n}$ and $B = \sum_{n=1}^{\infty} \frac{(-1)^n}{(3 + (-1)^n)^n}$ , then $\frac{A}{B}$ is…MediumSingle correct
27 Jun 2022, Shift 1 · Q3If $x=\sum_{n=0}^{\infty} a^n$ , $y=\sum_{n=0}^{\infty} b^n$ , $z=\sum_{n=0}^{\infty} c^n$ , where a, b, c are in A.P. and $|a|<1$ , $|b|<1$ ,…MediumSingle correct
28 Jun 2022, Shift 2 · Q25Let for $n=1, 2, \ldots, 50$ , $S_n$ be the sum of the infinite geometric progression whose first term is $n^2$ and whose common ratio is…HardNumerical value
26 Aug 2021, Shift 1 · Q67If the sum of an infinite GP $a, ar, ar^2, ar^3, \ldots$ is 15 and the sum of the squares of its each term is 150, then the sum of…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.