1. Essential Questions Series and Summation Notation
How do we find the terms of an arithmetic sequence?
How do we find the sum of an arithmetic series?
Holt McDougal Algebra 2
Holt Algebra 2

2. Finding the sum of a series with many terms can be tedious
Finding the sum of a series with many terms can be tedious. You can derive formulas for the sums of some common series.
In a constant series, such as , each term has the same value.
The formula for the sum of a constant series is as shown.

3. A linear series is a counting series, such as the sum of the first 10 natural numbers.
Examine when the terms are rearranged.

4. Notice that 5 is half of the number of terms and 11 represents the sum of the first and the last term, This suggests that the sum of a
linear series is , which can be written as
Similar methods will help you find the sum of a quadratic series.

6. When counting the number of terms, you must include both the first and the last. For example,
has six terms, not five.
k = 5, 6, 7, 8, 9, 10
Caution

7. Using Summation Formulas
Evaluate the series. 1.
Constant series
Method 1 Use the summation formula.
Method 2 Expand and evaluate.
There are 7 terms.

8. Using Summation Formulas
Evaluate the series. 2.
Linear series
Method 1 Use the summation formula.
Method 2 Expand and evaluate.

9. Using Summation Formulas
Evaluate the series. 3.
Quadratic series
Method 1 Use the summation formula.
Method 2 Use a calculator.
n(n + 1)(2n + 1) 6 =
12(12 + 1)(2 · ) 6 =
(156)(25) 6 =
= 650

10. Using Summation Formulas
Evaluate the series. 4.
Constant series
Method 2 Expand and evaluate.
Method 1 Use the summation formula. =
60 items
There are 60 terms.
= nc = 60(4) = 240
= 240

11. Using Summation Formulas
Evaluate the series. 5.
Linear series
Method 1 Use the summation formula.
Method 2 Expand and evaluate.
= = 120

12. Using Summation Formulas
Evaluate the series. 6.
Quadratic series
Method 1 Use the summation formula.
Method 2 Use a calculator.
n(n + 1)(2n + 1) 6 =
10(10 + 1)(2 · ) 6 =
(110)(21) 6 =
= 385

13. Lesson 5.2 Practice B