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Question

If the sum of first m terms of an AP is (2m2+3m) then what is its second term?

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Solution

Let SmSm denotes the sum of the first m terms of the AP.

Therefore,
Sm=(2m2+3m)


Sm1=2(m1)2+3(m1)
=2(m22m+1)+3(m1)
=2m2m1

Now,

mth term of the AP, am=SmSm1
Therefore,am=(2m2+3m)(2m2m1)=4m+1

Putting m = 2, we get

a2=4×2+1=9

Hence, the second term of the AP is 9.


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