Question

Which function represents the sequence 4, 12, 36, 108, ..., where n is a positive whole number?

Answer 1

f(n) = 4
`(3)^(n-1)`

Explanation:

there is a common ratio between consecutive terms in the sequence , that is

`(12)/(4)` =
`(36)/(12)` =
`(108)/(36)` = 3

this indicates the sequence is geometric, represented by

f(n) = a₁
`(r)^(n-1)`

a₁ is the first term and r the common ratio

here a₁ = 4 and r = 3 , then

f(n) = 4
`(3)^(n-1)`