# How do you find the first five terms of the geometric sequence for which a_1=-2 and r=3?

Feb 20, 2017

$\text{The first five terms are: } - 2 , - 6 , - 18 , - 54 , - 162$

#### Explanation:

A GP has the form

$a , a r , a {r}^{2} , a {r}^{3} , \ldots$

$\text{where " a="first term" , r="common ratio}$

in this case

${a}_{1} = a = - 2 , r = 3$

$1 s t = - 2$

$2 n d = - 2 \times 3 = - 6$

$3 r d = - 6 \times 3 = - 18$

$4 t h = - 18 \times 3 = - 54$

$5 t h = - 54 \times 3 = - 162$

$\text{The first five terms are: } - 2 , - 6 , - 18 , - 54 , - 162$