Question

Given the recursive formula for an arithmetic sequence find the explicit formula.

Answer 1

A recursive formula is a function of the previous term. The "an-1" is the term that comes before "an".
an arithmetic sequence just adds or subtracts the same number (common difference, d) between terms. looking at the recursive formula it is -9
-35, -44, -53, -62, .....

The explicit formula is a function of the terms place "n" in the sequence. This is written as :
an = a1 + d(n-1)
fill in
a1 = -35 and d = -9

an = -35 - 9(n-1)
expand to
an = -35 - 9n + 9
an = -26 - 9n