# What is the value of the fourth term in a geometric sequence for which a_1 = 15 and r = 1/3?

Jul 13, 2016

${a}_{4} = \frac{5}{9}$

#### Explanation:

The standard geometric sequence is.

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{a , a r , a {r}^{2} , a {r}^{3} , \ldots \ldots} \textcolor{w h i t e}{\frac{a}{a}} |}}}$
where the first term is represented by a, and each term of the sequence is obtained by multiplying the previous term by r, the common ratio.
The nth term is $\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}_{n} = a {r}^{n - 1}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

Here a = ${a}_{1} = 15 \text{ and } r = \frac{1}{3}$

$\Rightarrow {a}_{4} = 15 \times {\left(\frac{1}{3}\right)}^{3} = 15 \times \frac{1}{27} = \frac{5}{9}$