In an AP it is given that Sn = qn2 and Sm = qm2 . Prove that Sq = q^3 .

Given: Sn = qn2

, Sm = qm2

To prove: Sq = q3
Put n = 1 we get
a = q …… equation 1
Put n = 2
2a + d = 4q ……equation 2
Using equation 1 and 2 we get
d = 2q