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`