# How do you find the first 3 terms of the geometric sequence with a5 = -192 a9 = 1,536?

Aug 4, 2016

It seems there is a problem with this question. SHould it not be the 8th term which is 1536?

#### Explanation:

Divide the two terms - their general form and their values:

${a}_{9} / {a}_{5} = \frac{a {r}^{8}}{a {r}^{4}} = \frac{1536}{-} 192$

$\frac{\cancel{a} {r}^{8}}{\cancel{a} {r}^{4}} = \frac{1536}{-} 192$

${r}^{4} = - 8 = \left(- {2}^{3}\right)$

$r = {\left(- 2\right)}^{\frac{3}{4}} \text{ sub r to find a}$

${a}_{5} = a {r}^{4} = - 192$

$a {\left({\left(- 2\right)}^{\frac{3}{4}}\right)}^{4} = - 192$

$a {\left(- 2\right)}^{3} = - 192$

$a = - \frac{192}{-} 8 = 24$

Now we have $a \mathmr{and} r$