ALEX Classroom Resource

  

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

  Classroom Resource Information  

Title:

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

URL:

 https://flexbooks.ck12.org/cbook/ck-12-precalculus-concepts-2.0/section/12.1/related/lesson/describing-the-pattern-and-writing-a-recursive-rule-for-a-sequence-alg-ii/#

Content Source:

 Other
CK-12
Type: Informational Material

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

Content Standard(s):
Mathematics
MA2019 (2019)
Grade: 9-12
Applications of Finite Math
11. 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
Unpacked Content
Evidence Of Student Attainment:
Students:
  • -Use inductive counting methods to find recursive patterns and explicit formulas.
Teacher 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.
Diverse Learning Needs:
Mathematics
MA2019 (2019)
Grade: 9-12
Applications of Finite Math
12. 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.
Unpacked Content
Evidence Of Student Attainment:
Students:
  • Find the next term in a sequence such as the Fibonacci sequence, the triangular numbers, and pentagonal numbers.
  • Describe the recursion pattern that builds a sequence.
  • Hypothesize a formula to find the nth term in a sequence.
Teacher 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.
Diverse Learning Needs:
Tags: fibonacci sequence, formula, pattern, recursive, sequence, series
License Type: Custom Permission Type
See Terms: https://www.ck12info.org/terms-of-use/
For full descriptions of license types and a guide to usage, visit :
https://creativecommons.org/licenses
AccessibilityText Resources: Content is organized under headings and subheadings
Comments
  This resource provided by:  
Author: Hannah Bradley
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