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:
a_{n}
=
128
,
S_{n}
=
255
and
r
=
2
a_{n}
=
128
∴
a
r^{n-1}
=
128
⇒
a2^{n-1}
=
128
a2^{n}=256
.......... (i)
Also,
S_{n}
=
255
⇒
a
(
r^{n}
−
1)/(
r
−
1
)
=
255
⇒
a
(
2^{n}
−
1
)/(2-1)
=
255
⇒
a2^{n }- a =255
(
256
a
−
1
)
=
255
[Using (i)]
⇒
256
−
a
=
255
⇒
a
=
256
−
255
⇒
a
=
1