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Question

The sum of r terms of an AP is 2r2+3r. The nthterm is ___.


A

2n1

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B

4n+1

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C

3n1

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D

3n+1

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Solution

The correct option is B

4n+1


Given, Sr=(2r2+3r), the sum upto r terms of an AP.
We know that the nth term of AP is
Tn=SnSn1.
Sn=2n2+3n and
Sn1=2(n1)2+3(n1).

Tn=SnSn1
=2n2+3n[2(n22n+1)+3n3]
=2n2+3n2n2+4n23n+3 =4n+1

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