Question

How do you find the explicit formula for the following sequence 2, 4, 6, 8,...?

Answer 1

`a_n = a_1+2(n-1) = 2+2(n-1)`

Explanation:

Each term is 2 greater than the term before it. Thus for any given term, `a_n`, our equation is:

`a_n = 2n`

We can write this in a form closer to standard, by noting that `a_1=2`, so we can make it dependent on `a_1`..

`a_n = a_1+2(n-1) = 2+2(n-1)`