Question

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

Answer 1

`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 = 20 / 4 = 100 / 20 = 5`

`a_8 = 4 * 5^(8-1) = 4 * 5^7 = 312,500`