# How to Evaluate Recursive Formulas for Sequences

To specify a sequence, like any other function, we specify its domain and rule.

In general terms, the sequence rule is called sequence general sentence.

The general statement of a sequence is actually a rule through which each member of the domain corresponds to a member of the range set, that is, the general statement produces the statements of the sequence for each value of changes.

The general sentence of a sequence is represented by the symbol \(a_n\).

Evaluating the recursive formula of a sequence uses the recursive relation and the initial value(s) to find the value of each expression in the sequence.

To better understand this issue, let’s use an example. Consider the recursive formula for the sequence {\(a_n\)} where the recursive relation \(a_n=a_{(n-1)}+4\) and the initial value \(a_1 = 2\).

To find \(a_2\), put \(n=2\) and \(a_1=2\) into the recursive relation: \(a_2 = a_{(2-1)}+4=a_1+2=2+4=6\)

We continue the same process to find the next terms:** **

\(a_3 =a_{(3-1)}+4=a_2+2=6+4=10\)

\(a_4= a_{(4-1)}+4=a_3+2 =10+4=14\)

\(a_5=a_{(5-1)}+4=a_4+2=14+4=18\)

Therefore, the order of evaluations will be as follows: {\(2, 6, 10, 14, 18\)}.

Important note: In some cases, evaluating the recursive formula for large values of n may be impractical because it requires a lot of time or computing power.

## Related to This Article

### More math articles

- Types of Graphs
- How to Solve Powers of Products and Quotients? (+FREE Worksheet!)
- The Best TSI Math Worksheets: FREE & Printable
- How to Add and Subtract Integers: Word Problems
- DAT Quantitative Reasoning Math FREE Sample Practice Questions
- How to Use Grid Models to Convert Fractions to Percentages?
- How to Complete the Table of Division Two-Digit Numbers By One-digit Numbers
- 8th Grade RISE Math Worksheets: FREE & Printable
- How to Graph Absolute Value Function?
- Slope Fields Simplified: Understanding the Core of Differential Equations

## What people say about "How to Evaluate Recursive Formulas for Sequences - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.