Question

Find the sum of the grometric series: 16, -4, 1, -1/4...
(A) 4415/320
(B) 4095/320
(C) 64/5
(D) 16,383/1280
Im stuck- thanks for your help!

Answer 1

Given series 16 , -4 , 1 , -1/4 ...

Common ratio (r )  = T₂/T₁

r = -4/16 = -1/4

First term a  = 16

Formula for sum of infinity terms in geomeric series = a /(1-r )

Where | r | < 1

Sum = 16/(1-(-1/4))

= 16/(1+1/4)

= 16/(5/4)

Sum = 64/5

Opton C is correct choice.