(Q23).Which of the following are G.P. ? If they are G.P, write three more terms,
(ii)
1
3
, -
1
6
,
1
12
, ......
Given: t
1
=
1
, t
2
= -
1
, t
3
=
1
, .....
1
3
, -
1
6
,
1
12
, ......
t
2
t
1
=
-1
1
=
-1
×
=
-
t
3
t
2
=
1
-1
=
1
×
-
=
-
∴ r =
t
2
t
1
=
t
3
t
2
= ........ =
-
Hence the ratio is common between any two successive terms.
∴
1
3
, -
1
6
,
1
12
, ....... is G.P.
where a =
1
and r = -
1
a
4
= a.r
3
=
1
× (
-1
)
3
=
1
×
-1
=
-
a
5
= a.r
4
=
1
× (
-1
)
4
=
1
×
1
=
1
a
6
= a.r
5
=
1
× (
-1
)
5
=
1
×
-1
=
-
Clear