A geometric progression with first term 3 is such that the sum of the first three terms is 9. Find all possible values of the common ratio.
The first term of the geometric progression is 3, the next term is 3r, and the third term is 3r2.
What are the possible r-values if the sum of these three terms is 9?
3 + 3r + 3r2 = 9
1 + r + r2 = 3 [divide by 3]
r2+ r - 2 = 0 [subtract 3 from both sides and rearrange]
(r - 1)(r + 2) = 0
Either r = 1 or r = -2