# How do you write the first five terms of the geometric sequence a_1=1, r=1/2?

Jul 26, 2017

$1 , \frac{1}{2} , \frac{1}{4} , \frac{1}{8} , \frac{1}{16}$

#### Explanation:

Geometric sequences are defined by the formula $a {r}^{n - 1}$ where $a$ is the first term and $r$ is the common ratio (i.e. the second term divided by the first term or third divided by second).

When $n = 1$, $a {r}^{n - 1}$ becomes $1 \times {\left(\frac{1}{2}\right)}^{1 - 1} = 1 \times 1$ (anything to the power of zero is one).

When $n = 2$, $a {r}^{n - 1}$ becomes $1 \times {\left(\frac{1}{2}\right)}^{2 - 1} = 1 \times \frac{1}{2}$ and so on.

Jul 26, 2017

$1 , \frac{1}{2} , \frac{1}{4} , \frac{1}{8} , \frac{1}{16}$

#### Explanation:

$\text{the standard terms of a geometric sequence are}$

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

$\text{where a is the first term and r the common ratio}$

$\text{to obtain a term in the sequence multiply the previous}$
$\text{term by r}$

$\text{here "a=a_1=1" and } r = \frac{1}{2}$

${a}_{1} = 1$

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

${a}_{3} = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

${a}_{4} = \frac{1}{4} \times \frac{1}{2} = \frac{1}{8}$

${a}_{5} = \frac{1}{8} \times \frac{1}{2} = \frac{1}{16}$