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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. Inductive reasoning: Making conclusions based on patterns you observe.

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3.5 Arithmetic Sequences as Linear Functions

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  1. 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

  2. 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

  3. 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.

  4. Find the next two numbers in each pattern and describe the pattern • 2, 5, 8, 11,… • 2, 4, 6, 8,… • 1, 9, 17, 25, …

  5. Determine whether the sequence is an arithmetic sequence if so what is the pattern? -4, -2, 0, 2,…

  6. Determine whether the sequence is an arithmetic sequence if so what is the pattern? -26, -22, -18, -14,…

  7. Determine whether the sequence is an arithmetic sequence if so what is the pattern? 1, 4, 9, 25, …

  8. Determine whether the sequence is an arithmetic sequence if so what is the pattern?

  9. Find the nth term a1= first term of sequence d= common difference **** n must be positive ****

  10. Write an equation for the nth term of the arithmetic sequence -12, -8, -4, 0, …

  11. Find the 9th term of the sequence

  12. Which term of the sequence is 32?

  13. 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?

  14. 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

  15. Write an arithmetic sequence on a blank piece of paper.

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