Display Title
Definition--Sequences and Series Concepts--Explicit Formula
Display Title
Explicit Formula for a Sequence
Topic
Sequences and Series
Definition
An explicit formula for a sequence provides a direct way to calculate any term in the sequence.
Description
An explicit formula for a sequence is a mathematical expression that allows for the direct computation of any term in the sequence without needing to know the previous terms. This concept is fundamental in the study of sequences and series and is widely used in various mathematical applications.
In real-world applications, explicit formulas are used in financial calculations, such as determining the future value of investments or calculating loan payments. They are also used in computer algorithms for efficient data processing. Algebraically, an explicit formula for an arithmetic sequence can be expressed as
an = a1 + (n − 1)d
and for a geometric sequence as
an = a1 ⋅ r(n − 1)
Understanding explicit formulas is essential for math education as it helps students develop skills in recognizing and analyzing patterns. It provides a foundation for more complex 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 • Sequences |
| Copyright Year | 2021 |
| Keywords | data analysis, arithmetic sequence, common difference, definitions, glossary terms, geometric sequence, common ratio |
