Question

what is the common difference if sn is square of number of terms

Answer 1

Let a be the first term, d be the common difference and n be the number of terms.
Then, sum is
$\frac{n}{2} (2a + (n - 1)d) \\ given \: \: it \: \: is \: \: equal \: \: to \: \: {n}^{2} \\ i.e. \: \: \frac{n}{2} (2a + (n - 1)d) = {n}^{2} \\ 2a + (n - 1)d = 2n \\ d = \frac{2(n - a)}{n - 1}$