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

Apr 23, 2017

$2 , - 6 , 18 , - 54 , 162$

#### Explanation:

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

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

$\text{where r is the common ratio}$

$r = {a}_{2} / {a}_{1} = {a}_{3} / {a}_{2} = \ldots \ldots = \frac{{a}_{n}}{a} _ \left(n - 1\right)$

To obtain a term in the sequence multiply the previous term
by r

$\Rightarrow {a}_{1} = 2$

$\Rightarrow {a}_{2} = 2 \times - 3 = - 6$

$\Rightarrow {a}_{3} = - 6 \times - 3 = 18$

$\Rightarrow {a}_{4} = 18 \times - 3 = - 54$

$\Rightarrow {a}_{5} = - 54 \times - 3 = 162$