JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 27 June 2022, Shift 1, Maths Q3

Question 3 of 90 in this shift, Maths question 3 of 30, Section A.

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

|c|<1

abc \neq 0

, then :

(1) $x, y, z$ are in A.P.
(2) $x, y, z$ are in G.P.
(3) $\frac{1}{x}, \frac{1}{y}, \frac{1}{z}$ are in A.P.Official answer
(4) $\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1-(a+b+c)$

Official answer

Option 3

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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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.