# Write a rule for the nth term of the geometric sequence and then find a_5 given a_4=−3,r=−2

Write a rule for the nth term of the geometric sequence and then find ${a}_{5}$ given ${a}_{4}=-3,r=-2$
You can still ask an expert for help

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

the terms in a standard geometric sequence are
$a,ar,a{r}^{2},a{r}^{3},......,a{r}^{n-1}$
where a is the first term and r the common ratio
the nth term is
$•x{a}_{n}=a{r}^{n-1}$
${a}_{4}=a{r}^{3}=-3⇒a=\frac{-3}{{\left(-2\right)}^{3}}=\frac{-3}{-8}=\frac{3}{8}$
$⇒{a}_{n}=\frac{3}{8}{\left(-2\right)}^{n-1}$
$⇒{a}_{5}=\frac{3}{8}{\left(-2\right)}^{4}=\frac{3}{8}×16=6$