Question

if the sum of first q term of an AP is 2q+3qsquare . what is the common difference

Answer 1

put q=1 to get first term a1= s1 =3+2=5
Now put q=2 to get s2=4+12=16
a2= s2-s1=16-5=11
Common difference= a2-a1=6

Answer 2

the common difference is 6
$sq = 2q + {3q}^{2} \\ s1 = 2(1) + {3(1)}^{2} \\ s1 = 2 + 3 \\ s1 = 5 = a1 \\ s2 = 2(2) + {3(2)}^{2} \\ s2 = 4 + 3(4) \\ s2 = 4 + 12 = 16 \\ an = sn - sn - 1 \\ a2 = s2 - s2 - 1 \\ a2 = s2 - s1 \\ a2 = 16 - 5 = 11 = a2 \\ a2 - a1 = d \\ 11 - 5 = 6 = d$
hope this helps you quickly