Question

Write the recursive formula for the sequence

37, 67, 97, 127, 157

Answer 1

The recursive formula for this arithmetic sequence would be
`a_(1) = 37`,
`a_(i) = a_(i-1) + 30`.

Explanation:

A recursive formula is a formula that defines each term of a sequence using the preceding term(s). Recursive formulas must always state the initial term, or terms, of the sequence, as well as an equation defining
`a_(i)` in terms of preceding terms. Since the first term of this sequence is 37, that means
`a_(1) = 37`. The pattern in this arithmetic sequence between each term in ascending order would be 30 more than the previous term, so you can create the function
`a_(i) = a_(i-1) + 30`. So the recursive formula for this arithmetic sequence would be
`a_(1) = 37` and
`a_(i) = a_(i-1) + 30`.