 # Recursive Formulas for Sequences

Related Topics:
Lesson Plans and Worksheets for Algebra I
Lesson Plans and Worksheets for all Grades
More Lessons for Algebra I
Common Core For Algebra I

Examples, solution, and videos to help Algebra I students learn how to work on recursive formulas.

### New York State Common Core Math Algebra I, Module 3, Lesson 2

Worksheets for Algebra I, Module 3, Lesson 2 (pdf)

Lesson 2 Summary

Recursive Sequence: An example of a recursive sequence is a sequence that
(1) is defined by specifying the values of one or more initial terms and
(2) has the property that the remaining terms satisfy a recursive formula that describes the value of a term based upon an expression in numbers, previous terms, or the index of the term.

An explicit formula specifies the nth term of a sequence as an expression in n.

A recursive formula specifies the nth term of a sequence as an expression in the previous term (or previous couple of terms).

Exercise

2. Ben made up a recursive formula and used it to generate a sequence. He used B(n) to stand for the nth term of his recursive sequence.

a. What does B(3) mean?
b. What does B(m) mean?
c. If B(n + 1) = 33 and B(n) = 28 , write a possible recursive formula involving B(n + 1) and B(n) that would generate 28 and 33 in the sequence.
d. What does 2B(7) + 6 mean?
e. What does B(n) + B(m) mean?
f. Would it necessarily be the same as B(n + m)?
g. What does B(17) - B(16) mean?

For each sequence, write either a recursive formula.
a) 1, -1, 1, -1, 1, -1, ...
b) 12, 23, 34, 45, ...

4. For each sequence below, an explicit formula is given. Write the first 5 terms of each sequence. Then, write a recursive formula for the sequence.

a) an = 2n + 10 for n ≥ 1
b) an = (1/2)n-1 for n ≥ 1

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.