if 359=sum 17 how can the unknown next number be 966=sum 21

Answer 1

The question is mangled, but if you want to say that

S17 = 359
S21 = 966

for an arithmetic sequence, then just solve

17/2 (2a+16d) = 359
21/2 (2a+20d) = 966

For a geometric sequence, you need

a(r^17-1)/(r-1) = 359
a(r^21-1)/(r-1) = 966

In either case, the answers are not simple.