Question

Find the 6th term of a geometric sequence with t1 = 7 and t9 = 45,927.

Answer 1

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.

Answer 2

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