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Byju's Answer
Standard X
Mathematics
Sum of n Terms
If the third ...
Question
If the third term of a G.P. is 12 and its sixth term is 96, find the sum of 9 terms.
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Solution
Given that:
T
3
=
12
and
T
6
=
96
T
3
=
12
⇒
a
r
2
=
12
......... (1)
T
6
=
96
a
r
5
=
96
........ (2)
divide (2) by (1):
a
r
5
a
r
2
=
96
12
∴
r
3
=
8
r
3
=
2
3
∴
r
=
2
Consider,
a
r
2
=
12
a
(
2
)
2
=
12
∴
a
×
4
=
12
∴
a
=
3
Now, let us find
S
9
.
S
n
=
a
(
r
n
−
1
)
r
−
1
S
9
=
3
(
2
9
−
1
)
2
−
1
=
3
(
512
−
1
)
1
=
3
(
511
)
∴
S
9
=
1533
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