1. Problems of the Day 4x + y = 43 x – 8y = – 44 6x + y = 42 3/21/2018
Write the equation for the line in Standard Form.
m = – 4, through (8, 11)
4x + y = 43
through (12, 7) and (– 4, 5)
x – 8y = – 44
3. m = – 6, x-intercept 7
6x + y = 42

2. 3-7 Recursive Formulas For Arithmetic Sequences

3. 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:

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

5. 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:

6. Example Consider the sequence generated by
Describe the sequence in words.
B) Write the 1st five terms of the sequence.
This is an arithmetic sequence with first term 2000 and constant difference 40. A constant difference of 40 means that each term is 40 more than the previous term.
2000, 2040, 2080, 2120, 2160

7. 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.

8. Graph of an Arithmetic Sequence
Discrete Domain
Constant Increase
Collinear Points
Discrete Domain (x-values)
will be 1, 2, 3, 4, 5, …

9. 3-8 Explicit Formulas For Arithmetic Sequences

10. Arithmetic Sequences Explicit Formula
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.

11. Explicit Formula n 1 2 3 4 # of d 1 2 3 an 1000 1000+3000=40001 2 3 an
1000
=4000
=7000
=10000

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

13. Examples
Find the 40th term of the arithmetic sequence 100,97,94,91,…..
2. 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?
The 40th term is – 17.
There are 23 rows of seats in the concert hall.

14. Assignment Worksheets 3-7 & 3-8. Pages 177-178 #’s 3, 4, 6, 8-11.
3/21/2018
Assignment
Worksheets 3-7 & 3-8.
Pages #’s 3, 4, 6, 8-11.
Pages #’s 4-6, 9-11, 14, 15, 17, 18a, 18b.
Quiz on Sections 3-4 & 3-5 next class!!!!
Chapter 3 Test Coming SOON!!!! STUDY!