Question

For the GP 3, 6, 12, ..., find the 8th term and the sum of the first 8 terms.

Solution

1. The first term is a = 3 and the common ratio is r = 6/3 = 2.
2. The nth term is ar^(n - 1), so the 8th term is 3 x 2^7 = 3 x 128 = 384.
3. The sum of n terms is a(r^n - 1) / (r - 1), so S8 = 3(2^8 - 1) / (2 - 1) = 3 x 255 = 765.
4. Therefore, the 8th term is 384 and the sum of the first 8 terms is 765.