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Common Core For Algebra I

Examples, videos, and solutions to help Algebra I students learn the meaning and notation of recursive sequences.

New York State Common Core Math Module 1, Algebra I, Lesson 26, Lesson 27

### New York State Common Core Math Algebra I, Module 1, Lesson 26, Lesson 27

Worksheets for Algebra 1

Lesson 27 Student Outcomes

Lesson Plans and Worksheets for Algebra I

Lesson Plans and Worksheets for all Grades

More Lessons for Algebra I

Common Core For Algebra I

Examples, videos, and solutions to help Algebra I students learn the meaning and notation of recursive sequences.

New York State Common Core Math Module 1, Algebra I, Lesson 26, Lesson 27

Lesson 26 Student Outcomes

Students learn the meaning and notation of recursive sequences in a modeling setting.

Following the modeling cycle, students investigate the double and add 5 game in a simple case in order to understand the statement of the main problem.

Definitions

A **sequence** can be thought of as an ordered list of elements. The elements of the list are called the terms of the sequence.

An example of a** recursive sequence** is a sequence that is defined by

(1) specifying the values of one or more initial terms, and

(2) having the property that the remaining terms satisfy a recurrence relation that describes the value of a term based upon an algebraic expression in numbers, previous terms, or the index of the term.

Exit Ticket

The following sequence was generated by an initial value a_{0} and recurrence relation a_{i+1} = 2a_{i} + 5, for i ≥ 0

1. Fill in the blanks in the sequence:

(___, 29, ___, ___, ___, 539, 1083).2. In the sequence above, what is a_{0}? What is a_{5}?

Lesson 27 Student Outcomes

Students learn the meaning and notation of recursive sequences in a modeling setting.

Students use recursive sequences to model and answer problems.

Students create equations and inequalities to solve a modeling problem.

Students represent constraints by equations and inequalities and interpret solutions as viable or non-viable options in a modeling context.

Lesson 27 Summary

The formula, a_{n} = 2^{n}(a_{0} + 5) - 5 describes the nth term of the “double and add 5” game in terms of the starting number a_{0} and n. Use this formula to find the smallest starting whole number for the “double and add 5 game” that produces a result of 10,000,000 or greater in 15 rounds or less.

Lesson 27 Exit Ticket

Write a brief report about the answers you found to the Double and Add 5 game problems. Include justifications for why your starting numbers are correct.

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