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Byju's Answer
Standard X
Mathematics
Sum of N Terms of an AP
Find the sum ...
Question
Find the sum to n terms of the series
1
2
+
3
2
+
5
2
+
…
to
n
terms.
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Solution
let
T
n
be
n
t
h
term of the series
thus
T
n
=
(
2
n
−
1
)
2
=
4
n
2
−
4
n
+
1
∑
T
n
=
∑
4
n
2
−
4
n
+
1
=
4
∑
n
2
−
4
∑
n
+
∑
1
=
4
n
(
n
+
1
)
(
2
n
+
1
)
6
−
4
n
(
n
+
1
)
2
+
n
=
n
(
n
+
1
)
(
2
3
(
2
n
+
1
)
−
2
)
+
n
=
n
(
n
+
1
)
(
4
n
+
2
−
6
3
)
+
n
=
n
3
(
n
+
1
)
(
4
n
−
4
)
+
n
=
4
3
n
(
n
+
1
)
(
n
−
1
)
+
n
=
4
3
n
(
n
2
−
1
)
+
n
=
n
3
(
4
n
2
−
4
+
3
)
=
n
.
(
2
n
−
1
)
(
2
n
+
1
)
3
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