Question

How do you write an nth term rule for `5,-5/3,5/9,-5/27,...` and find `a_6`?

Answer 1

See below

Explanation:

Geometric sequence explicit formula:
`a_n = a_1(r)^(n-1)`

Determine `r` which is the decay factor:
`r=-5/3*1/5= -1/3`

Substitute into the equation for the rule:
`a_n = 5(-1/3)^(n-1)`

For the sixth term:
`a_6 = 5(-1/3)^(6-1)=-5/243`