(Q14).The 4th term of a geometric progression is
2
3
and the seventh term is
16
81
. Find the geometric series.
Given: In a G.P.
a
4
=
⇒ a.r
3
=
.........(1)
a
7
=
⇒ a.r
6
=
.........(2)
equation (2)
equation (1)
=
a.r
6
a.r
3
=
⇒ r
6-3
=
×
=
⇒ r
3
= (
)
3
∴ r =
Now substituting r =
in equation (1)
we get,
a (
)
3
=
⇒ a =
×
×
×
=
9
4
∴ The G.P. is a, ar, ar
2
, ar
3
, .......
9
4
,
9
4
×
;
9
4
× (
)
2
; ........ =
9
4
,
, 1, ........
Clear