Question

Which recursive formula can be used to represent the sequence 2,4,6,8,10,...?

Answer 1

Use the formula y+2=x over and over or just +2 or counting by twos

Answer 2

$a_{n}$ represents the next number in the sequence

we can see that there is a common difference between each of the numbers:
4-2=2
6-4=2
8-6=2
10-8=2

$a_{n-1}$ represents the previous number in the sequence

$a_{n}=a_{n-1}+2$ this is the recursive formula for this equation

The last thing we need to do it double check the formula by plugging in numbers

$a_{1}=a_{1-1}+2 \\ a_{1}=a_{0}+2 \\ 2=0+2 \\ 2=2$

we will skip to the last known number and check that one too

$a_{5}=a_{5-1}+2 \\ a_{5}=a_{4}+2 \\ 10=8+2 \\ 10=10$