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 first term .Submitted on 8/7/2024 | Answered by Vandana Rana

Answer :

The answer to this question will be as following: an = 128 ,
Sn = 255
and r = 2
an = 128
∴ a rn-1 = 128
⇒ a2n-1 = 128
a2n=256 .......... (i)
Also, Sn = 255
⇒ a ( rn − 1)/( r − 1 ) = 255
⇒ a ( 2n − 1 )/(2-1) = 255
⇒ a2n - a =255
( 256 a − 1 ) = 255 [Using (i)]
⇒ 256 − a = 255
⇒ a = 256 − 255
⇒ a = 1