Question

If the sum of the first q terms of an AP is 2q+3q2, what is it's common difference ?

Answer 1

put q=1

s1 = 2 + 3 = 5

put q =2

s2 = 4 + 12 = 16

so common difference is 16 - 5 = 11

Answer 2

Sq=2q+3q2

q=1

S1=2(1)+3(1)2

S1=2+3=5

S1=a1=5

q=2

S2=2(2)+3(2)2

S2=4+12=16

S2=a1+a2

16=5+a2

a2=16-5=11

d=a2-a1

=11-5

=6