Question

A certain arithmetic sequence has the following explicit formula for the nth term:

an = 2 + (n - 1)(6)

The same sequence has the following recursive formula:

an = an-1 + _____

What number belongs in the blank space in the recursive formula?

Answer 1

\[a_{n-1}=2+((n-1)-1)6=2+6(n-1)-6=a_{n}-6\Rightarrow a_n=a_{n-1}+6\]