\(k, a_2, a_3\) and \(k, b_2, b_3\) are both nonconstant geometric sequences with different common ratios. We have \(a_3-b_3=3(a_2-b_2).\). Find the sum of the common ratios of the two sequences.
Im not quite sure how to do this problem.
\(k, rk, r^2k \qquad \qquad k, Rk, R^2k \)
\(r^2k - R^2k = 3(rk-Rk)\\ r^2 - R^2 = 3(r-R)\\ (r-R)(r+R) = 3(r-R)\\ r+R=3 \)
The sum of the ratios is 3