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Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 3

#### Display Title

Math Example--Sequences and Series--Finding the Recursive Formula of an Arithmetic Sequence: Example 3

# Finding the Recursive Formula of an Arithmetic 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 Difference: The common difference is found by subtracting the first term from the second term.
- Write the Recursive Formula: The recursive formula for an arithmetic sequence is:

a_{n} = a_{n - 1} + d

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

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: [8, 13, 18, 23, 28]

First term (a₁) = 8

Common difference (d) = 13 - 8 = 5

Recursive formula: a_{n} = a_{n - 1} + 5

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 | arithmetic sequences, recursive formula |