The fifth term of a G.P. is
16
and 9th term is . Find the 4th term.
243
3
town and the first to
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Answer:
Let a be the first term and r be the common ratio of the GP.
For a GP, the nth term is given by T
n
=ar
n−1
Given, T
5
=9
=>ar
5−1
=9
=>ar
4
=9 -- (1)
And,
T
12
=
243
1
=>ar
12−1
=
243
1
=>ar
11
=
243
1
-- (2)
Dividing eqn 2 by eqn 1, we get
=>r
7
=
243×9
1
=
3
5
×3
2
1
=
3
7
1
=>r=
3
1
Substituting in eqn 1, we get
a×(
3
1
)
4
=9
a=729
And T
9
=ar
9−1
=729×(
3
1
)
8
=
9
1
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