Display Title
Definition--Sequences and Series Concepts--Recursive Formula
Display Title
Recursive Formula
Topic
Sequences and Series
Definition
A recursive formula defines each term of a sequence using the preceding term(s).
Description
A recursive formula is a fundamental concept in mathematics, representing a way to define each term of a sequence using the preceding term(s). This concept is essential in various mathematical and scientific applications, including computer science and algorithm design.
In real-world applications, recursive formulas are used in algorithm design, particularly in recursive algorithms that solve problems by breaking them down into smaller subproblems. They are also used in financial calculations to model compound interest. Algebraically, a recursive formula for an arithmetic sequence can be expressed as
an = an − 1 + d
and for a geometric sequence as
an = an − 1 ⋅r
Understanding recursive formulas is crucial for math education as it helps students develop skills in recognizing and analyzing patterns defined by previous terms. It provides a foundation for more advanced topics in algebra and calculus, and aids in developing problem-solving skills.
For a complete collection of terms related to sequences and series click on this link: Sequences and Series Collection
| Common Core Standards | CCSS.MATH.CONTENT.6.SP.B.4, CCSS.MATH.CONTENT.HSF.IF.A.3, CCSS.MATH.CONTENT.HSF.BF.A.2, CCSS.Math.CONTENT.HSF.LE.A.2, CCSS.MATH.CONTENT.HSF.BF.A.1.A |
|---|---|
| Grade Range | 6 - 9 |
| Curriculum Nodes |
Algebra • Sequences and Series • Series |
| Copyright Year | 2021 |
| Keywords | data analysis, arithmetic sequence, common difference, definitions, glossary terms, geometric sequence, common ratio |
