Question

What are the explicit equation and domain for an arithmetic sequence with a first term of 3 and a second term of -9?

Answer 1

Difference between -9 and 3:
-9 - 3 = -12.

Common difference is -12.

Explicit equation is therefore


`a_n = 3 - 12(n-1) = 15 - 12n`

The domain is


`\{ n \mid n \in \mathbb{N} \}` (all natural numbers)
or equivalently
`\{ n \mid n = 1,2,3,4,...\}`