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