# How do you write a rule for the nth term of the geometric term and then find a_6 given r=3, a_1=2?

Oct 30, 2017

From the reference Geometric Progression we use the general form:

${a}_{n} = {a}_{1} {r}^{n - 1}$

#### Explanation:

Substitute ${a}_{1} = 2$ and $r = 3$ into the general form:

${a}_{n} = 2 {\left(3\right)}^{n - 1}$

Substitute $n = 6$

${a}_{6} = 2 {\left(3\right)}^{6 - 1}$

${a}_{6} = 2 {\left(3\right)}^{5}$

${a}_{6} = 486$