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Question

Very-Short and Short-Answer Questions

If the sum of first m terms of an AP is (2m2 + 3m) then what is its second term? [CBSE 2011]

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Solution

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

Sm=2m2+3mSm-1=2m-12+3m-1 =2m2-2m+1+3m-1=2m2-m-1
Now,
mth term of the AP, am = Sm − Sm − 1
am=2m2+3m-2m2-m-1=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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