Solveeit Logo
Login

Question

Question: If 3 +\(\frac { 1 } { 4 }\)(3 + d) + \(\frac { 1 } { 4 ^ { 2 } }\)(3 + 2d)+…… ¥ = 8, then the value ...

If 3 +14\frac { 1 } { 4 }(3 + d) + 142\frac { 1 } { 4 ^ { 2 } }(3 + 2d)+…… ¥ = 8, then the value of d is

A

9

B

5

C

1

D

None of these

Answer

9

Explanation

Solution

Sum of ¥ terms of A.G.P = a1−r\frac { \mathrm { a } } { 1 - \mathrm { r } } +

3(1−14)\frac { 3 } { \left( 1 - \frac { 1 } { 4 } \right) } +  d. 14(1−14)2\frac { \text { d. } \frac { 1 } { 4 } } { \left( 1 - \frac { 1 } { 4 } \right) ^ { 2 } } = 8

̃ 36 + 4d = 72

d = 9