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

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Common Core For Algebra I

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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