Question

In an A.P. if the sum of $n$ term is $n^2$ then find the common difference of the A.P.

Answer 1

Given in an A.P. if the sum of $n$ term is $n^2=S_n$ (let).

We know that the first term is $a_1=S_1=1$.

Now, $S_2=a_1+a_2=2^2=4.$

Now, $a_2=S_2-S_1=4-1=3$.

So we've, $a_1=1,a_2=3$.

Now common difference is $a_2-a_1=3-1=2$.