If 8=3+1/4(3+p)+frac 1 4 2 (3+2 p)+frac 1 4 3 (3+3 p)+ldots ∞ then the value of p is

Mathematics · Sequence and Series

JEE Main 2024 — 27 January, Shift 1 — Question 23

If $8=3+\frac{1}{4}(3+p)+\frac{1}{4^{2}}(3+2 p)+\frac{1}{4^{3}}(3+3 p)+\ldots \infty$ then the value of $p$ is

Answer: 9

Numerical answer — enter this value.

Step-by-step solution

$8=\frac{3}{1-\frac{1}{4}}+\frac{p \cdot \frac{1}{4}}{\left(1-\frac{1}{4}\right)^{2}}$ (sum of infinite terms of G.P $\left.=\frac{\mathrm{a}}{1-\mathrm{r}}+\frac{\mathrm{dr}}{(1-\mathrm{r})^{2}}\right)$

$\Rightarrow \frac{4 \mathrm{p}}{9}=4 \Rightarrow \mathrm{p}=9$

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Exam: JEE Main 2024
Paper: 27 January, Shift 1
Subject: Mathematics
Chapter: Sequence and Series
Topic: Geometric Progression

The number of common terms in the progressions 4,9,14,19, ldots ldots , up to 25^ th term and 3,6,9,12 , ......., up to 37^ th term is :

Answer: 9

Step-by-step solution

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