If an arithmetic progression sum of first n terms is ${2n}^2+3n$ .Its common difference is:

The correct option is D.$4$

Sum of first n terms of an AP$=2n^2+3n=S_n$

To find the common difference,

We know that sum of n terms of an AP is$S_n$

$S_n=\frac{n}{2}[a+(n-1\left)d\right]$

$S_1=a${a= first term of AP}

$2(1{)}^2+3(1)=a$

$a=5$

$S_2=a+(a+d)$

$2(2{)}^2+3(2)=5+5+d$

$d=4$

Therefore common difference is equal to $4$