# What is the 8th term of the geometric sequence 4, 20, 100,...?

Jun 1, 2018

color(brown)(a_8 = 312,500

#### Explanation:

Nth term of geometric sequence ${a}_{n} = a {r}^{n - 1}$

$a = 4 , {a}_{2} = 20 , {a}_{3} = 100$

$r = {a}_{2} / a = {a}_{3} / {a}_{2} = \frac{20}{4} = \frac{100}{20} = 5$

${a}_{8} = 4 \cdot {5}^{8 - 1} = 4 \cdot {5}^{7} = 312 , 500$