Answer:
is given that the first term of G.P is a
1
=3 and the second term is a
2
=6, therefore,
r=
a
1
a
2
=
3
6
=2
We know that the formula for the nth term of an G.P is T
n
=ar
n−1
, where a is the first term, r is the common ratio.
It is given that the first term is a=3, the nth term is T
n
=1536 and the common ratio is r=2, thus,
T
n
=ar
n−1
⇒1536=3×(2)
n−1
⇒
3
1536
=2
n−1
⇒2
n−1
=512
⇒2
n−1
=2
9
⇒n−1=9
⇒n=9+1=10
Hence, the 10th term is 1536.
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