# How do you find a_8 for the geometric sequence 4, -12, 36,...?

Oct 16, 2016

${a}_{8} = - 8 , 748$

#### Explanation:

To find the value of a term in a GP, you need to know:

${a}_{1} , r \mathmr{and} n$

${a}_{1} = 4$

$r = \frac{- 12}{4} = - 3$

for ${a}_{8} , n = 8$

${a}_{n} = {a}_{1} \times {r}^{n - 1} \text{ } \leftarrow$ the general term

${a}_{8} = 4 \times {\left(- 3\right)}^{7}$

${a}_{8} = - 8 , 748$