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Byju's Answer
Standard X
Mathematics
Sum of n Terms
Show that the...
Question
Show that the ratio of the sum of first n terms of a G.P. to the sum of terms form
(
n
+
1
)
t
h
to
(
2
n
)
t
h
term is
1
r
n
.
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Solution
Sum of first n terms,
S
n
=
a
(
1
−
r
n
)
1
−
r
Sum of terms from (n+1)th to 2n th term is,
S
2
n
−
S
n
=
a
(
1
−
r
2
n
)
1
−
r
−
a
(
1
−
r
n
)
1
−
r
=
a
(
r
n
−
r
2
n
)
1
−
r
Ratio,
=
a
(
1
−
r
n
)
1
−
r
a
(
r
n
−
r
2
n
)
1
−
r
=
1
−
r
n
r
n
−
r
2
n
=
1
−
r
n
r
n
(
1
−
r
n
)
=
1
r
n
Hence proved.
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