Question

1. Which function describes the sequence 2,4,6,8......? *

O F(1) = 2; f(n) = f(n-1) + 2 for n > 2
O F (1) = 2; f(n) = f (n − 1) – 2 for n > 2
OF (1) = 2; f(n − 1) = f (n) + 2 for n > 3
Of(1) = 2; f(n − 1) = f (n) – 2 for n > 3

Answer 1

`f(1) = 2`

`f(n) = f(n-1) + 2` where
`n\geq 2`

Explanation:

Given

2,4,6,8...

Required

Which function determines the sequence

Represent the terms with n where n is 1,2,3....

Analyzing each term:

`f(1) = 2`

`f(2)= 4 = 2 + 2 = f(1) +2`

`f(3)= 6 = 4 + 2 = f(2) +2`

`f(4)= 8 = 6 + 2 = f(3) +2`

Notice that each term is an addition of the previous term and 2

In other words:

`f(n) = f(n-1) + 2`

However, the function is only effective for values of n greater than or equal to 2

So:
`n\geq 2`