Question

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

Answer 1

Answer:

$f(1) = 2$

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

Step-by-step 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: $n\geq 2$