1. Warm-up
1. Find 3f(x) + 2g(x)
2. Find g(x) – f(x)
3. Find g(-2)

2. Go over homework

3. Sequences
A sequence is a function whose domain is a set of consecutive whole numbers. So the domain in any sequence is {1,2,3,4…} The values in the range are called the terms of the sequence. A sequence can be specified by an equation or a rule.

4. Arithmetic Sequence
A sequence of terms that have a common difference between them

5. Determine if the sequence is arithmetic.
Example:
-22, -15, -8, -1, …
Arithmetic
d = 7

6. Determine if the sequence is arithmetic.
Example:
½, ¼, 1/8, 1/16, …
Not Arithmetic

7. Determine if the sequence is arithmetic.
Example:
7, 4, 1, -2, -5
Arithmetic
d = -3

8. Explicit Formula
Formula used to find the nth term of a sequence

9. Explicit Formula for Arithmetic Sequence

10. Find the common difference, the explicit formula, and the tenth term.
3, 9, 15, 21, …
d = 6
an = 6n – 3
a10 = 57

11. Find the common difference, the explicit formula, and the twentieth term.
7, 4, 1, -2, …

12. Applications
The marching band has 14 marchers in the front row, 16 in the second row, 20 in the fourth row, and so on. How many marchers are in the 15th row?

13. Applications
Several friends want to go on a rafting trip. The cost of the trip per person is in the chart.
How much would it cost for 9 people to go?
Passengers 1 2 3 4
Cost
$75
$100
$125
$150

14. Applications
A bag of cat food weighs 18 pounds at the beginning of day 1. Each day, the cats are fed 0.5 pounds of food. How much does the bag of cat food weigh at the beginning of day 30?

15. Recursive Formula
A recursive rule for a sequence defines the nth term by relating it to one or more previous terms.

16. Recursive Formula for Arithmetic Sequence

17. Find the first four terms of the sequence.
Example:
a1 = 3
an = an-1 + 2
3, 5, 7, 9

18. Write the recursive formula for the following sequence:
3,6,9,12…
What are the next 3 terms?

19. Classwork
Worksheet

20. Homework
Worksheet