Question

What is the 7th term of the geometric sequence 4, –20, 100, …?

Answer 1

`color(maroon)(a_7 = 4 * (-5)^6 = 62500`

Explanation:

`a = 4, a_2 = -20, a_3 = 100`. To find `a_7`

Common ratio `r = a_2 / a = a_3/a_2 = -20/4 = 100/-20 = -5`

`n^(th)` term of G S `a_n = a r^(n-1)`

`:. a_7 = a * r^6`

`color(maroon)(a_7 = 4 * (-5)^6 = 62500`