Question 401429
{{{a[3] = a[1]*r^2 = (a[1])^2}}}==> {{{a[1]  =r^2}}}.

Now {{{a[5] = a[1]*r^4 = 64}}}==> {{{r^2*r^4 = r^6 = 64}}} ==> r = -2, 2.

==> {{{a[1] = 4}}}.

Incidentally there are two G.P.'s that satisfy the initial conditions.