Let 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 G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to-

Mathematics · Sequence and Series

JEE Main 2024 — 31 January, Shift 2 — Question 9

Let $2^{\text {nd }}, 8^{\text {th }}$ and $44^{\text {th }}$ , terms of a non-constant A.P. be respectively the $1^{\text {st }}, 2^{\text {nd }}$ and $3^{\text {rd }}$ terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to-

Option A:
980
Option B:
960
Option C:
990
Option D:
970
Correct

Answer: D

Step-by-step solution

$1+\mathrm{d}, 1+7 \mathrm{~d}, 1+43 \mathrm{~d}$ are in GP

$(1+7 d)^{2}=(1+d)(1+43 \mathrm{~d})$

$1+49 \mathrm{~d}^{2}+14 d=1+44 d+43 \mathrm{~d}^{2}$

$6 d^{2}-30 d=0$

$\mathrm{d}=5$

$\begin{aligned}\mathrm{S}_{20} & =\frac{20}{2}[2 \times 1+(20-1) \times 5] &=10[2+95] & =970\end{aligned}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 31 January, Shift 2
Subject: Mathematics
Chapter: Sequence and Series
Topic: Geometric Progression