Question

What is the 9th term of the geometric sequence where a1 = -6 and a6 = -6,144?

Answer 1

The general formula for geometric is: \[
a_n = a_1r^{n-1}
\]And we were given: \[
a_1 = -6
\]And \[
a_6 =a_1r^{6-1} = -6144
\]

Answer 2

Combining this information we have: \[
-6 r^{5} = -6144
\]We just need to solve for \(r\) and then find \(a_9\)

Answer 3

\[ \large
a_9 = a_1r^{9-1}
\]