# How do you write the first five terms of the geometric sequence a_1=1, r=1/3?

Mar 6, 2017

$1 , \frac{1}{3} , \frac{1}{9} , \frac{1}{27} , \frac{1}{81}$

#### Explanation:

The standard terms in a geometric sequence are.

$a , a r , a {r}^{2} , a {r}^{3} , \ldots . , a {r}^{n - 1}$

where a is the first term and r the common ratio.

Each term in the sequence is obtained by multiplying the previous term by r, the common ratio.

${a}_{1} = 1$

$\Rightarrow {a}_{2} = 1 \times \frac{1}{3} = \frac{1}{3}$

$\Rightarrow {a}_{3} = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$

$\Rightarrow {a}_{4} = \frac{1}{9} \times \frac{1}{3} = \frac{1}{27}$

$\Rightarrow {a}_{5} = \frac{1}{27} \times \frac{1}{3} = \frac{1}{81}$

$\text{The first five terms are } 1 , \frac{1}{3} , \frac{1}{9} , \frac{1}{27} , \frac{1}{81}$