Question

Find an explicit rule for the nth term of the sequence.

-2, -8, -32, -128

Answer 1

`a_(n)` = - 2
`(4)^(n-1)`

Explanation:

There is a common ratio between consecutive terms , that is

r = - 8 ÷ - 2 = - 32 ÷ - 8 = - 128 ÷ - 32 = 4

This indicates the sequence is geometric with nth term

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

Here a₁ = - 2 and r = 4 , then explicit formula is

`a_(n)` = - 2
`(4)^(n-1)`