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Standard XII
Mathematics
Sigma n
A geometric p...
Question
A geometric progression has the first term
a
, common ratio
r
and sum to infinity
S
. A second geometric progression has first term
a
, common ratio
2
r
and sum to infinity
3
S
. Find the value of
r
.
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Solution
First G.P:
a
,
r
Second G.P:
a
,
2
r
the sum of infinite G.P=
a
1
−
r
s
=
a
1
−
r
.
.
.
.
.
.
.
.
.
.
(
1
)
3
s
=
a
1
−
2
r
.
.
.
.
.
.
.
.
.
.
(
2
)
e
q
(
2
)
e
q
(
1
)
=
a
1
−
2
r
a
1
−
r
=
3
s
s
3
=
1
−
r
1
−
2
r
r
=
2
5
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