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Byju's Answer
Standard XII
Mathematics
Geometric Progression
Find the comm...
Question
Find the common ratio of the
G
.
P
.
whose first and last terms are
25
and
1
625
, respectively and the sum of the
G
.
P
.
is
19531
625
.
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Solution
Given that:-
First term of G.P.
(
a
)
=
25
Last term of G.P.
(
n
)
=
1
625
As we know that,
n
t
h
term of a G.P. is given by-
a
n
=
a
r
n
−
1
1
625
=
25
×
r
n
−
1
⇒
r
n
=
r
15625
.
.
.
.
.
(
1
)
Sum of G.P.
=
19531
625
[
Given
]
Sum of
n
terms of G.P.-
S
n
=
a
(
1
−
r
n
)
r
−
1
[
∵
r
<
1
]
∴
25
(
1
−
r
15625
)
1
−
r
=
19531
625
⇒
15625
−
r
=
19531
−
19531
r
⇒
19530
r
=
19531
−
15625
⇒
r
=
3906
19530
=
1
5
Hence the common ratio of the given G.P. is
1
5
.
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