# How do you write the first five terms of the geometric sequence a_1=6, r=-1/4?

Aug 9, 2017

$6 , - \frac{3}{2} , \frac{3}{8} , - \frac{3}{32} , \frac{3}{128}$

#### Explanation:

$\text{the terms in a geometric sequence are}$

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

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

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

${a}_{1} = 6$

${a}_{2} = 6 \times - \frac{1}{4} = - \frac{3}{2}$

${a}_{3} = - \frac{3}{2} \times - \frac{1}{4} = \frac{3}{8}$

${a}_{4} = \frac{3}{8} \times - \frac{1}{4} = - \frac{3}{32}$

${a}_{5} = - \frac{3}{32} \times - \frac{1}{4} = \frac{3}{128}$