MA19.FM.12

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

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.

Vocabulary

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

COS Examples

Example: Write a sequence of the first 10 triangular numbers and hypothesize a formula to find the nth triangular number.

Aligned Learning Resources

The Fibonacci Sequence
Recursive Formulas: Fibonacci Sequence
12.1 Describing the Pattern and Writing a Recursive Rule For a Sequence
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