The ith term is given by T(i) = 2i-1
Let us denote the Sum to n terms as S(n).
= Sum(i= 1 to n) (2i-1)
= 2*Sum(i= 1 to n) i) - n
= n^2 + n -n
Consequently, the required sum upto any term of the given sequence is always a perfect square.