31Geometric sequence, 8th term and sum

A geometric sequence has first term 3 and common ratio 2. Find the 8th term and the sum of the first 8 terms.

The 8th term is 384, and the sum of the first 8 terms is 765. Using a_n = ar^(n−1): a_8 = 3·2^7 = 384. Using S_n = a(r^n−1)/(r−1): S_8 = 3(2^8−1)/1 = 3(255) = 765, confirmed by adding all eight terms.