Classroom Resource

12.1 Describing the Pattern and Writing a Recursive Rule For a Sequence

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

This informational material will introduce the concept of recursive sequences and explain how to write recursive formulas. The Fibonacci Sequence is introduced. Practice questions with a PDF answer key are provided

Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.11

Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.

Unpacked Content

UP:MA19.FM.11

Vocabulary

  • Difference equation
  • Recursive process
  • Recursive formula
  • Sequences
  • Series

Knowledge

Students know:

  • How to use inductive counting methods such as lists.

Skills

Students are able to:

  • Use inductive counting methods to collect data for conjecturing.
  • Find recursive formulas from collected data.
  • Develop explicit formulas.

Body

  1. Find patterns in application problems involving series and sequences, and develop recursive and explicit formulas as models to understand and describe sequential change.
    Examples: fractals, population growth
Mathematics (2019) Grade(s): 09-12 - Applications of Finite Mathematics

MA19.FM.12

Determine characteristics of sequences, including the Fibonacci Sequence, the triangular numbers, and pentagonal numbers.

Unpacked Content

UP:MA19.FM.12

Vocabulary

  • Recursive process
  • Recursive formula
  • Triangular numbers
  • Pentagonal numbers
  • Fibonacci sequence
  • Closed Formula

Knowledge

Students know:

  • How to recognize a pattern.

Skills

Students are able to:

  • Identify the pattern in a sequence.
  • Explain why a pattern occurs.

Understanding

Students understand that:

  • The recursion process can be applied to many situations.
  • A sequence lists the solutions of a set of related problems.
  • Formulas can be hypothesized by identifying how the problems are related.

Body

  1. Determine characteristics of sequences, including the Fibonacci Sequence, the triangular numbers, and pentagonal numbers.
    Example: Write a sequence of the first 10 triangular numbers and hypothesize a formula to find the nth triangular number.
Link to Resource
https://flexbooks.ck12.org/cbook/ck-12-precalculus-concepts-2.0/section/12.1/re…

CR Resource Type

Informational Material

Resource Provider

CK-12
Accessibility

Accessibility

Text Resources: Content is organized under headings and subheadings
License

License Type

Custom

Custom License Type (URL)

https://www.ck12info.org/terms-of-use/
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