Question

If the sum of first $m$ terms of an A.P. is $2m^2+3m$, then what is its second term?

Answer 1

$sm=2m^2+3m$

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

$=2(m^2+1-2m)+3m-3$

$=2m^2+2-4m+3m-3$

$=2m^2-m-1$

$\therefore sm-sm-1=2m^2-+3m-(2m^2-m-1)=2m^2+3m-2m^2+m+1$

$=4m+1$

General term$=am=4m+1$

Second term$=a_2=4\left(2\right)+1=8+1=9$