study guides for every class

that actually explain what's on your next test

Recursive formula

from class:

Algebra and Trigonometry

Definition

A recursive formula defines each term of a sequence using the preceding term(s). It typically includes an initial condition and a recurrence relation.

congrats on reading the definition of recursive formula. now let's actually learn it.

ok, let's learn stuff

5 Must Know Facts For Your Next Test

  1. A recursive formula requires at least one initial condition to specify the first term of the sequence.
  2. The general form for an arithmetic sequence's recursive formula is $a_{n} = a_{n-1} + d$, where $d$ is the common difference.
  3. For a geometric sequence, the recursive formula is $a_{n} = a_{n-1} \cdot r$, where $r$ is the common ratio.
  4. Recursive formulas can be used to model real-world problems such as population growth and financial calculations.
  5. To find a specific term in a sequence defined by a recursive formula, you must know all prior terms up to that point.

Review Questions

  • What information do you need to start using a recursive formula?
  • How does the recursive formula differ for arithmetic and geometric sequences?
  • Can you provide an example of how to use a recursive formula to find the third term in an arithmetic sequence with $a_1=2$ and $d=3$?
© 2024 Fiveable Inc. All rights reserved.
AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
Glossary
Guides