Series and Summation Notation

1. Series and Summation Notation Essential Questions • 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. The formula for the sum of a constant series is as shown. 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 3 + 3 + 3 + 3 + 3, each term has the same value.

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 5is half of the number of terms and 11represents the sum of the first and the last term, 1 + 10. 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. Caution 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

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

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

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

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

11. Using Summation Formulas Evaluate the series. Linear series 5. Method 1 Use the summation formula. Method 2 Expand and evaluate. = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 = 120

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

13. Lesson 5.2 Practice B