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Recursive Challenge Problem - The Double and Add 5 Game


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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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.


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 a0 and recurrence relation ai+1 = 2ai + 5, for i ≥ 0

1. Fill in the blanks in the sequence:

(___, 29, ___, ___, ___, 539, 1083).

2. In the sequence above, what is a0? What is a5?

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, an = 2n(a0 + 5) - 5 describes the nth term of the “double and add 5” game in terms of the starting number a0 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.

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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