In a sequence if an=5(3^n-1).prove that it is a GP.find the first term and the common ratio
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Step-by-step explanation:
ANSWER
Given,
S
n
=
3
n
4
n
−3
n
⇒S
n
=(
3
4
)
n
−1
S
n−1
=(
3
4
)
n−1
−1
T
n
=S
n
−S
n−1
=(
3
4
)
n
−1−(
3
4
)
n−1
+1
=(
3
4
)
n−1
(
3
4
−1)
∴T
n
=
4
1
(
3
4
)
n
T
1
=
4
1
(
3
4
)
1
=
3
1
T
2
=
4
1
(
3
4
)
2
=
9
4
T
3
=
4
1
(
3
4
)
3
=
27
16
T
1
T
2
=
9
4
×
1
3
=
3
4
T
2
T
3
=
27
16
×
4
9
=
3
4
As
T
1
T
2
=
T
2
T
3
, given series is in G.P
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