Question

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

Answer 1

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

∴ s_m = 2m² +3m

`⇒ s_(m-1) = 2 (m -1)^2 +3 (m-1) = 2( m^2 - 2m +1) +3 (m-1) = 2m^2 - 3-1`

Now, 

`m^(th)  "term of A"P,  a_m = s_m - s_(m-1)`
∴ `a_3 = ( 2m^2 + 3m ) - (2m^2 - m -1 ) = 4m +1`

Putting m = 2,we get

`a_2 = 4 xx 2 +1 = 9`

Hence, the second term of the AP is 9.