Question

How many terms of the geometric progression 1 + 4 + 16 + 64 + …….. must be added to get sum equal to 5461?

Answer 1

Given G.P. : 1 + 4 + 16 + 64 + ...........

Here,

First term, a = 1

Common ratio, r = `4/1 = 4`  ...(∵ r > 1)

Let the number of terms to be added = n

Then, S_n = 5461

`=> (a(r^n - 1))/(r - 1) = 5461`

`=> (1(4^"th" - 1))/(4 - 1) = 5461`

`=>(4^"th" - 1)/3 = 5461`

`=>` 4^th – 1 = 16383

`=>` 4^th = 16384

`=>` n = 7

Hence, required number of terms = 7