Find the sum of n²+2n
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Answer:
The sum of n terms formula is given by,
S
n
=
2
n
[2a+(n−1)d]
S
n
=n
2
+2n....(2)
Comparing equation (1) & (2), we get
2
n
[2a+(n−1)d]=n
2
+2n
2an+n
2
d−nd=2n
2
+4n
(2a−d)n+n
2
d=4n+2n
2
On comparing factors of n
2
d=2
On comparing factors of n in equation (3), we have
2a−d=4
2a=4+d
2a=4+2
2a=6
a=3
Therefore, the first term, a=3 and the common difference, d=2.
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