6th term of gp is 24 and its 13th term is 3/16 find 8th term of gp
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n
th
term of a G.Pt
n
=ar
n−1
6
th
term of a G.Pt
6
=ar
6−1
=ar
5
=24…(1)
13
th
term of a G.Pt
13
=ar
13−1
=ar
12
=
16
3
…(2)
Dividing (1) by (2)
⇒
ar
12
ar
5
=
16
3
24
=
3
24×16
=8×16
⇒
r
7
1
=2
3
×2
4
=2
7
⇒r
7
=
2
7
1
∴r=
2
1
We have ar
5
=24
⇒a=
r
5
24
⇒a=
(
2
1
)
5
24
=24×32=768
∴a=768,r=
2
1
We know that, t
n
=ar
(n−1)
∴25
th
term of a G.Pt
25
=768×(
2
1
)
25−1
t
25
=
2
24
768
t
25
=
2
16
3
∴25
th
term is 3×2
−16
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