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3.5 Arithmetic Sequences as Linear Functions. Objective: 1) Use inductive reasoning in continuing number patterns 2) Write rules for arithmetic sequences 3) Relate arithmetic sequences to linear functions. Vocabulary. Inductive reasoning: Making conclusions based on patterns you observe.

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3 5 arithmetic sequences as linear functions

3.5 Arithmetic Sequences as Linear Functions

Objective:

1) Use inductive reasoning in continuing number patterns

2) Write rules for arithmetic sequences

3) Relate arithmetic sequences to linear functions

vocabulary
Vocabulary
  • Inductive reasoning: Making conclusions based on patterns you observe.
  • Sequence: a set of numbers in a specific order
  • Terms: the numbers in a sequence
vocabulary continued
Vocabulary Continued
  • Arithmetic Sequence: A numerical pattern that increase or decrease at a constant rate or value.
  • Common Difference: The difference between the terms in a sequence. Represented by the letter d.
find the next two numbers in each pattern and describe the pattern
Find the next two numbers in each pattern and describe the pattern
  • 2, 5, 8, 11,…
  • 2, 4, 6, 8,…
  • 1, 9, 17, 25, …
determine whether the sequence is an arithmetic sequence if so what is the pattern
Determine whether the sequence is an arithmetic sequence if so what is the pattern?

-4, -2, 0, 2,…

determine whether the sequence is an arithmetic sequence if so what is the pattern1
Determine whether the sequence is an arithmetic sequence if so what is the pattern?

-26, -22, -18, -14,…

determine whether the sequence is an arithmetic sequence if so what is the pattern2
Determine whether the sequence is an arithmetic sequence if so what is the pattern?

1, 4, 9, 25, …

find the nth term
Find the nth term

a1= first term of sequence

d= common difference

**** n must be positive ****

you try
You Try

Consider the arithmetic sequence

3, -10, -23, -36, …

  • Write an equation for the nth term of the sequence
  • Find the 15th term in the sequence
  • Which term of the sequence is –114?
arithmetic sequences as functions
Arithmetic Sequences as Functions

Marisol is mailing invitations for her quinceanera. The arithmetic sequence $0.41, $0.82, $1.23, $1.64, … represents the cost of postage.

  • Write a function to represent this sequence