The sum of the first nine terms of a geometric sequence is 684 and the common ratio is -2. Find the first and eighth terms. [My answers are: 1st term=6.2 8th term:793.6]

Question

I'm not sure if a geometric progression is the same as a geometric sequence. Let me know if my answers are correct or how I should go about solving it.

Answer 1

a[1 + r + ...r⁸] = a(1 - ar⁹)/(1-r) where r = -2

684 = a[1 - (-2)⁹]/[1 - (-2)] = a(513/3) = 171a and a = 4

The first term is 4 and the 8th term is and the 8th term is -512