Introduction to Sequences

1. Introduction to Sequences Essential Questions • How do we find the nth term of a sequence? • How do we write rules for sequences? • How do we evaluate summation notation? Holt McDougal Algebra 2 Holt Algebra 2

2. Now that you have learned how to find the nth term of a sequence. Often we are also interested in the sum of a certain number of terms of a sequence. A seriesis the indicated sum of the terms of a sequence. Some examples are shown in the table.

3. Because many sequences are infinite and do not have defined sums, we often find partial sums. A partial sum, indicated by Sn, is the sum of a specified number of terms of a sequence.

4. A series can also be represented by using summation notation, which uses the Greek letter  (capital sigma) to denote the sum of a sequence defined by a rule, as shown.

5. Using Summation Notation Write the series with summation notation.

6. Using Summation Notation Write the series with summation notation.

7. Using Summation Notation Write the series with summation notation.

8. Using Summation Notation Write the series with summation notation.

9. Caution!

10. Evaluating a Series Expand the series and evaluate. Expand the series by replacing k. Evaluate powers.

11. Evaluating a Series Expand the series and evaluate. Expand the series by replacing k. Evaluate powers.

12. Evaluating a Series Expand the series and evaluate. Expand the series by replacing k. Evaluate powers.

13. Evaluating a Series Expand the series and evaluate. Expand the series by replacing k. Evaluate powers.

14. Lesson 5.1 Practice B