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Question

The sum of first n terms of an A.P is given by Sn=2n2+3n. Find the sixteenth term of the A.P

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Solution

Sn=n2(2a+(n1)d)
=n2(2ad)+n2d2=2n2+3n
2=d2=4 and 2ad2=3
2a=6+d=10
or, a=5.
a16=a+(1+1)d
=5+15×4=65.

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