1. Warm-up
L11-2 & L11-3 Obj: Students will be able to find the general term for arithmetic series

2. Is the given sequence arithmetic?
Arithmetic Sequences
LESSON 11-2
Additional Examples
Is the given sequence arithmetic?
a. 7, 10, 13, 16, . . .
b. The sequence of dots in the “triangles” shown below.

3. Practice

4. Write a recursive and explicit formula for each sequence
Find the 30th term for each
A. 34, 37, 40, 43,…
B. 0.1, 0.5, 0.9, 1.3,…

5. Arithmetic Sequences
LESSON 11-2
Additional Examples
Suppose you have already saved $75 toward the purchase of a new CD player and speakers. You plan to save at least $12 a week from money you earn at a part-time job. In all, what is the minimum amount you will have after 26 weeks?

6. Write an explicit formula for the following sequence:
Find the 24th term
Write a recursive formula for the following sequence:
Find the next three terms

7. Find the missing term of the arithmetic sequence 50, , 92.

8. Practice 1. -16, ___, 1 2. 5, ___, 21 3. 101, _____, -115
4. 2,___, ___,___,-22
5. 1,___, ___,___,-35
6. -17, ___,___,___,1

9. Obj: Students will be able to identify and generate geometric sequences

10. Find the next two terms 1. 1,2,4,8,… 2. 1,-2,4,-8,… 3. 10,4,1.6,.64,…
Practice
Find the next two terms
1. 1,2,4,8,…
2. 1,-2,4,-8,…
3. 10,4,1.6,.64,…

11. 1. Find the explicit formula for each sequence
1. Find the explicit formula for each sequence. Then generate the first 4 terms.
a1= 3, r = -2 2.
Find the explicit formula for each sequence.
Find the recursive formula for each sequence.
Then generate the first 4 terms.
a1= -1, r = 4

12. Practice a. Find the explicit formula for each sequence.
b. Find the recursive formula for each sequence
c. Then generate the first 4 terms.
1. a1 = 32, r = -.05
2. a1 = 9, r = 2

13. Ex: Find the missing term
1. -1, ___, -36
, ___, ___, ___, 5.12

14. Ex: Find the missing term
1. -1, ___, -36
, ___, ___, ___, 5.12

15. Geometric Sequences
LESSON 11-3
Additional Examples
Suppose you have equipment that can enlarge a photo to 120% of its original size. A photo has a length of 10 cm. Find the length of the photo after 5 enlargements at 120%.
You need to find the 6th term of the geometric sequence 10, 12, 14.4, . . .

16. geometric mean = 150,000 • 188,160 Use the definition.
Geometric Sequences
LESSON 11-3
Additional Examples
A family purchased a home for $150,000. Two years later the home was valued at $188,160. If the value of the home is increasing geometrically, how much was the home worth after one year?
geometric mean = ,000 • 188,160 Use the definition.
= 28,224,000,000 Multiply.
= 168,000 Take the square root.
Homework:
L11-2 (p. 618) #16-40e e 64, 66
L11-3 (p. 625 #14-30e 38-52e