The ith term is given by T(i) = 2i-1 Let us denote the Sum to n terms as S(n). Then, S(n) = Sum(i= 1 to n) (2i-1) = 2*Sum(i= 1 to n) i) - n = n^2 + n -n = n^2

Consequently, the required sum upto any term of the given sequence is always a perfect square.