# How do you write an nth term rule for r=1/3 and a_1=45?

Sep 14, 2016

${a}_{n} = 45 {\left(\frac{1}{3}\right)}^{n - 1}$

#### Explanation:

The rule for finding the nth term in a geometric sequence is.

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}_{n} = a {r}^{n - 1}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where a represents the 1st term.

here a = 45 and r$= \frac{1}{3}$

$\Rightarrow {a}_{n} = 45 \times {\left(\frac{1}{3}\right)}^{n - 1} = 45 {\left(\frac{1}{3}\right)}^{n - 1}$