9-4 Arithmetic Series
Objective
To define arithmetic series and find their sums
Lesson Vocabulary
- series
- finite series
- infinite series
- arithmetic series
- limits
Just as you found formulas for terms of sequences, you can find formulas for the sums of the terms of sequences.
Essential Understanding When you know two terms and the number of terms in a finite arithmetic sequence, you can find the sum of the terms.
A series is the indicated sum of the terms of a sequence. A finite series, like a finite sequence, has a first term and a last term, while an infinite series continues without end.
| Finite sequence | Finite series |
|---|---|
| 6, 9, 12, 15, 18 |
|
| Infinite sequence | Infinite series |
|---|---|
| 3, 7, 11, 15, … |
|
An arithmetic series is a series whose terms form an arithmetic sequence (as shown above). When a series has a finite number of terms, you can use a formula involving the first and last term to evaluate the sum.
Take Note Property: Sum of a Finite Arithmetic Series
The sum
where
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions