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