Standard Accessed: Students will analyze sequences, find sums of series, and use recursive rules.

Warm-up Check 4, 7, 12, 19 3, 10, 29 1, 8, 27, 64

Big Idea

Vocabulary Is a function whose domain is a set of consecutive integers. A sequence can be described by a rule that generates its nth term. The values in the range. Has a limited number of terms. Has an unlimited number of terms.

Vocabulary Is also called sigma notation.

Write terms of sequences EXAMPLE 1 SOLUTION (a) = 4, 9, 14, 19, 24, 29 (b) = -1, 1, 5, 13, 29, 61

Write rules for sequences EXAMPLE 2 SOLUTION

Exercise Julie, Jinny, John, and Joel at the beginning of the fall break, walked a kilometer in 9 minutes. At the end of the first week they walked a kilometer in 5 fewer seconds. At the end of the second week, they decreased their time by another 10 seconds. At the end of the third week, they decreased their time by 20 more seconds, and at the end of the fourth week, they decreased their time by another 40 seconds. Write a rule for the number of seconds they decreased their time by each week. Then graph the sequence for the first four weeks. EXAMPLE 3 Solving a Multi-Step Problem

Write series using summation notation EXAMPLE 4 SOLUTION Write the series using summation notation. Which series is finite? infinite? What is the nth term in each series?

Find the sum of a series EXAMPLE 5 SOLUTION

Study Strategy

Use a formula for a sum EXAMPLE 6 SOLUTION

Lesson 7.1 Define and Use Sequences & Series Homework: Honors – Homework Academic – Homework