1. 3-7 Recursive Formulas For Arithmetic Sequences
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3-7 Recursive Formulas For Arithmetic Sequences

2. 4/21/2017
If you buy a new car, you might be advised to have an oil change after driving 1000 miles and every 3000 miles thereafter. Then the following sequence gives the mileage when oil changes are required:

3. Arithmetic Sequences Arithmetic Sequence: Recursive Formula:
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Arithmetic Sequences
Arithmetic Sequence:
Sequence with a constant difference between terms. Here it was d = 3000
Recursive Formula:
Formula where each term is based on the term before it
Recursive Formula for an Arithmetic Seq:

4. 4/21/2017
If you buy a new car, you might be advised to have an oil change after driving 1000 miles and every 3000 miles thereafter. Then the following sequence gives the mileage when oil changes are required:

5. Example Consider the sequence generated by
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Example
Consider the sequence generated by
Describe the sequence in words
Write the 1st five terms of the sequence

6. 4/21/2017
Example
Briana borrowed $870 from her parents for airfare to Europe. She will pay them back at the rate of $60.00 per month. Let an be the amount she still owes after n months. Find a recursive formula for this sequence.

7. Graph of an Arith. Seq. Discrete Domain Constant Increase or Decrease
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Graph of an Arith. Seq.
Discrete Domain
Constant Increase or
Decrease
Collinear Points

8. 3-8 Explicit Formulas For Arithmetic Sequences
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3-8 Explicit Formulas For Arithmetic Sequences

9. Arithmetic Sequences Explicit Formula 4/21/2017
Formula where any term can be found by substituting the number of that term.
We can develop an explicit formula for an Arithmetic Sequence from the recursive formula

10. Explicit Formula 4/21/2017 n 1 2 3 4 # of d 1 2 3 an 10001 2 3 an
1000
=4000
=7000
=10000

11. So, for our oil change example, the explicit formula looks like:
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So, for our oil change example, the explicit formula looks like:

12. 4/21/2017
Examples
Find the 40th term of the arithmetic sequence 100,97,94,91,…..
In a concert hall the 1st row has 20 seats in it, and each subsequent row has 2 more seats than the row in front of it. If the last row has 64 seats, how many rows are in the concert hall?