Question

Write an explicit formula for a_n, the nth term of the sequence 4, -20, 100, ...

Answer 1

`a_(n)` = 4
`(-5)^(n-1)`

Explanation:

There is a common ratio r between consecutive terms , that is

r = - 20 ÷ 4 = 100 ÷ - 20 = - 5

This indicates the sequence is geometric with nth term ( explicit formula )

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = 4 and r = - 5 , then

`a_(n)` = 4
`(-5)^(n-1)`