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Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 3

#### Display Title

Math Example--Sequences and Series--Finding the Recursive Formula of a Geometric Sequence: Example 3

# Finding the Recursive Formula of a Geometric Sequence: Example 3

## Topic

Sequences and Series

## Description

Process for Finding the Recursive Formula

- Identify the First Term: The first term of the sequence is denoted as a
_{1.} - Determine the Common Ratio: The common ratio r is found by dividing the second term by the first term.
- Write the Recursive Formula: The recursive formula for an arithmetic sequence is:

a_{n} = a_{n - 1}•r

where a_{n} is the nth term, a_{n - 1} is the previous term, and r is the common ratio.

Distinguishing Recursive from Explicit Formulas

- Recursive Formula: Defines each term based on the previous term(s). It requires knowing the initial term and is useful for generating terms sequentially.
- Explicit Formula: Allows direct computation of any term in the sequence without reference to previous terms. It is more efficient for finding terms far into the sequence.

Given Sequence

Sequence: [3, 9, 27, 81, 243]

First term (a₁) = 3

Common ratio (r) = 9 / 3 = 3

Recursive formula: a_{n} = a_{n - 1}•3

For a complete collection of math examples related to Sequences and Series click on this link: __Math Examples: Sequences and Series Collection.__

Common Core Standards | CCSS.MATH.CONTENT.HSF.BF.A.2 |
---|---|

Grade Range | 9 - 11 |

Curriculum Nodes |
Algebra• Sequences and Series• Sequences |

Copyright Year | 2022 |

Keywords | geometric sequence, recursive formula |