# How do you find the 7th term of the geometric sequence with the given terms a4 = 54, a5 = 162?

Jan 20, 2016

${a}_{7} = 1458$

#### Explanation:

Since this is a geometric sequence we know the following

${a}_{n} = {a}_{1} {r}^{n - 1}$ noticed we started at 1 that why we subtract 1 from n

the ratio $r = \frac{{a}_{n}}{{a}_{n - 1}}$

We are given

${a}_{4} = 54 \text{ " } {a}_{5} = 162$

We first, need to find $r$

$r = \frac{{a}_{5}}{{a}_{4}} = \frac{162}{54} = 3$

Then we can use the formula ${a}_{n} = {a}_{1} {r}^{n - 1}$

(but instead of finding ${a}_{1}$ , we will use ${a}_{4}$ we need to subtract 4 from the nth term

${a}_{7} = {a}_{4} {r}^{7 - 4}$

${a}_{7} = \left(54\right) {\left(3\right)}^{3}$

" a_7 = 1458