What is the common ratio and the ninth term for the following sequence:
\[
5,15,45,135, \ldots
\]
\[
r=
\]
\[
\mathrm{a}_{9}=
\]

Answer

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Answer

\(\boxed{r = 3, a_9 = 32,805}\)

Steps

Step 1 ：Find the common ratio by dividing the second term by the first term: \(r = \frac{15}{5}\)

Step 2 ：\(r = 3\)

Step 3 ：Use the formula for the nth term of a geometric sequence: \(a_n = a_1 * r^{(n-1)}\)

Step 4 ：Plug in the values: \(a_9 = 5 * 3^{(9-1)}\)

Step 5 ：\(a_9 = 5 * 3^8\)

Step 6 ：\(a_9 = 32805\)

Step 7 ：\(\boxed{r = 3, a_9 = 32,805}\)