If 8=3+ 14(3+p)+ 14^2(3+2p)+ 14^3(3+3p)+ … ,then the value of p is_____

Correct answer: 9. (9) 8= 31- 14+ p 14(1- 14)^2 (sum of infinite terms of A.G.P = a1-r+ dr (1-r )^2 ) ⇒ 4p9=4 ⇒p=9

JEE Previous Year Question

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

Topic: JEE PYQ

Answer: 9. Full step-by-step solution below.

Correct answer: 9

(9) 8 = \frac{3}{1 - \frac{1}{4}} + \frac{p \cdot \frac{1}{4}}{( 1 - \frac{1}{4} ) ^{2}} (sum of infinite terms of A.G.P = \frac{a}{1 - r} + \frac{dr}{( 1 - r ) ^{2}}) \Rightarrow \frac{4 p}{9} = 4 \Rightarrow p = 9