Question

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

Answer 1

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

Therefore,
$S_m=(2m^2+3m)$

⇒$S_{m-1}=2(m-1{)}^2+3(m-1)$
=$2(m^2-2m+1)+3(m-1)$
=$2m^2-m-1$

Now,

mth term of the AP, $a_m=S_m-S_{m-1}$
Therefore,$a_m=(2m^2+3m)-(2m^2-m-1)=4m+1$

Putting m = 2, we get

$a_2=4\times 2+1=9$

Hence, the second term of the AP is 9.