JEE Main 2022 · MathsMultiple choiceSingle correctMediumMulti-step

JEE Main 29 June 2022, Shift 1, Maths Q12

Question 12 of 90 in this shift, Maths question 12 of 30, Section A.

Let

\{a_n\}_{n=0}^{\infty}

be a sequence such that

a_0 = a_1 = 0

and

a_{n+2} = 2a_{n+1} - a_n + 1

for all

n \ge 0

. Then,

\sum_{n=2}^{\infty} \frac{a_n}{7^n}

is equal to :

(1) $\frac{6}{343}$
(2) $\frac{7}{216}$ Official answer
(3) $\frac{8}{343}$
(4) $\frac{49}{216}$

Official answer

Option 2

NTA final key (2022 Session 1).

Chapter: Sequences and Series
Topic: Arithmetico-Geometric Series
Idea tested: AGP Recurrence Relation

Same topic in other shifts

All Arithmetico-Geometric Series questions

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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.