Question

In an arithmetic sequence, `f(0) = 8` and #f(2) = 12. What are the first several terms of the sequence?

Answer 1

`f(n) = 8+2n` and so the sequence looks like

`8, 10, 12, 14, 16, 18, 20, 22, ...`

Explanation:

An arithmetic sequence is a sequence in which there is a constant difference between terms. That is,
`f(n) = a_0 + cn`
where `a_0` is the first term in the sequence, and `c` is the difference between terms.

In the given sequence, we have
`f(0) = a_0 = 8`
`f(2) = a_0+2c = 8+2c = 12`

As `8+2c = 12`, we have `2c = 4`, meaning `c = 2`

With that, we can easily calculate `f(n)` as `8+2n` or just add `2` over and over to come up with multiple terms quickly.