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3.5 Arithmetic Sequences as Linear Functions

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Presentation on theme: "3.5 Arithmetic Sequences as Linear Functions"— Presentation transcript:

1 3.5 Arithmetic Sequences as Linear Functions
10/17/16

2 CC State Standards F.BF.2 Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations and translate between the two forms.

3 New Terms Sequence – a set of numbers. 3, 5, 7, 9, 11, . . .
Terms of of the Sequence – a set of numbers in a specific order. 3, 5, 7, 9, 11, Is the sequence going up or down?

4 Terms The common difference (d) = 2.
Arithmetic Sequence – the difference between successive terms is constant. 3, 5, 7, 9, 11, . . . 5 – 3 = ? – 5 = ? – 7 = ? – 9 = ? Focus on what terms I am subtracting. Common Difference – the difference between the terms 5 – 3 = – 5 = – 7 = – 9 = 2 The common difference (d) = 2.

5 Determine whether each sequence is an arithmetic sequence
Determine whether each sequence is an arithmetic sequence. Write yes or no. 4, 9, 14, 19, . . . Find the common difference 18, 16, 15, 13, . . . Find the common difference

6 Determine whether each sequence is an arithmetic sequence
Determine whether each sequence is an arithmetic sequence. Write yes or no. -10 , - 7, - 4, 1, . . . Find the common difference -12.3, -9.7, -7.1, -4.5, . . . Find the common difference

7 Find the next three terms of each arithmetic sequence.
21, 19, 17, 15, . . Find the common difference. ___, ____, ____. .02, 1.08, 2.14, 3.2, . . . Find the common difference. ___, ___, ____.

8 Arithmetic Sequence Formula
an = a1 + d(n – 1) an is the nth term a1 is the first term of the sequence d is the common difference n is the positive integer Write an equation for the nth term of each arithmetic sequence. 1, 3, 5, 7, . . . Write the arithmetic sequence formula. Find the common difference Replace the common difference and first term in the formula

9 Write an equation for the nth term of each arithmetic sequence.
- 1, - 4, - 7 , - 10, . . . Write the arithmetic sequence formula Find the common difference Put the common difference and first term in the formula. Then simplify


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