Question

How do you write an explicit rule for the nth term of the sequence -1, 2, 5, 8...?

Answer 1

The general form for the nth term for an Arithmetic progression is:

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

where `a_1` is the first term in the progression, and `d` is the difference between each term:

We can see that `a_1 = -1` and the difference between all of the terms is `d = 3`, therefore, the equation for the nth term is:

`a_n = -1 + 3(n-1)`