1. Day 92 – Geometric sequences (day2)

2. Vocabulary
Two types of sequences were studied: Arithmetic Sequence: A sequence is called arithmetic if there is a real number d such that each term in the sequence is the sum of the previous term and d. Geometric Sequence: A sequence is called geometric if there is a real number r such that each term in the sequence is a product of the previous term and r.

3. List the first five terms of each sequence, and identify them as arithmetic or geometric.1. 2.

4. List the first five terms of each sequence, and identify them as arithmetic or geometric.1.
-2,2,6,10,14 Arithmetic 2.
Geometric

5. 3. 4.

6. 3.
–6, – 25, – 44, – 63, – 82 Arithmetic 4.
Geometric

7. nth term of an Geometric Sequence
Every geometric sequence can be defined using the explicit formula:
Where:
an nth term
a1 1st term
n term number
r common ratio

8. Word Problem 1
A rabbit population grew in the following pattern: 2, 4, 8, 16, If all the rabbits live and the pattern continues, how many rabbits will be in the 8th generation?

9. Solution

10. Problem
Consider the equation y = 150(2x ) a. Make a table x and y – values for whole-number x-values from 0 to 5. b. What do the numbers 150 and 2 in the equation tell you about the relationship? x 1 2 3 4 5 y

11. Answer Key
Consider the equation y = 150(2x ) a. Make a table x and y – values for whole-number x-values from 0 to 5. b. What do the numbers 150 and 2 in the equation tell you about the relationship? 150 is the initial value 2 is the growth rate x 1 2 3 4 5 y
150
300
600
1200
2400
4800

12. Word Problem 2
Fido did not have fleas when his owners took him to the kennel. The number of fleas on Fido after he returned from the kennel grew according to the equation f = 8(3n). Where f is the number of fleas returned from the kennel. (Fido left the kennel at week 0.) a. How many fleas did Fido pick up at the kennel? b. What is the growth factor for the number of fleas? c. How many fleas will Fido have after 10 weeks if he is not treated?

13. Answer Key
Fido did not have fleas when his owners took him to the kennel. The number of fleas on Fido after he returned from the kennel grew according to the equation f = 8(3n). Where f is the number of fleas returned from the kennel. (Fido left the kennel at week 0.) a. How many fleas did Fido pick up at the kennel? 8 b. What is the growth factor for the number of fleas? 3 c. How many fleas will Fido have after 10 weeks if he is not treated? 8(310) = 472,392