3.5 Arithmetic Sequences as Linear Functions

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3.5 Arithmetic Sequences as Linear Functions - PowerPoint PPT Presentation

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

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.
• Sequence: a set of numbers in a specific order
• Terms: the numbers in a sequence
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.
• 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?

-4, -2, 0, 2,…

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 pattern?

1, 4, 9, 25, …

Find the nth term

a1= first term of sequence

d= common difference

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

-12, -8, -4, 0, …

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

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