## anonymous one year ago Find the 6th term of a geometric sequence with t1 = 7 and t9 = 45,927.

1. kropot72

The formula for the n-th term of a geometric sequence is given by: $\large ar^{n-1}$ where a is the first term and r is the common difference. When we plug in the given values, and knowing the value of the ninth term, we can write: $\large 45927=7r^{9-1}...........(1)$ Now you need to solve equation (1) to find the value of r, the common difference.

2. kropot72

Rearranging equation (1) gives: $\large r^{8}=6561$ and the value of r is given by: $\large r=\sqrt[8]{6561}$