Question

The nth term of a G.P is 128 and the sum of its n terms is 255. If its common ratio is 2, then find its first term.

Please answer fast.

Answer 1

let the first term of G.P be a.
the common ratio r =2
nth term of GP is 128
a.rn-1=128a.rn=128.r
a.rn=128×2=256_(1)
sum of n terms of GP is 25
therefore
a.rn-1r-1=255a.rn-a2+1=255256-a1=255a=256-255a=1
thus the first term is 1.