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