Download 10.6 Geometric Sequences.notebook

10.6 Geometric Sequences.notebook
Bellwork
February 18, 2016
10.6 Geometric Sequences
Ellen is saving for graduate school. She can choose between an account that offers 3.0% interest compounded quarterly, or an account that offers 6% interest compounded semiannually. If she has $5000 to start with and has only 3 three years to invest, which account should she choose?
Jan 24­2:06 PM
Objectives:
TSW: 1. Determine if a sequence is geometric. 2. Find missing terms in a geometric sequence.
Nov 26­9:35 AM
Geometric Sequence:
A sequence in which each term after the first term is found by multiplying the previous term by a constant r, called the common ratio.
Common Ratio:
Example 1: Given the following sequence of numbers, decide whether it is geometric. If it is state the common ratio.
a. 1, 8, 16, 24, 32, ...
b. 64, 32, 16, 8, ...
The ratio of successive terms of a geometric sequence. c. 1, 2, 4, 14, 54, ...
Nov 26­9:35 AM
Nov 26­9:35 AM
Example 2: Find the common ratio and the next three terms in the geometric sequence.
a. 1, –8, 64, –512, ...
b. 64, 48, 36, 27, ....
r = ______; = ______, = ______, = ______
Nov 26­9:35 AM
r = ______; = ______, = ______, = ______
Writing an Explicit Formula for Geometric Sequences:
1. Determine that the sequence is geometric.
2. Identify the common ratio. 3. Create an explicit formula using the first term in the sequence and the common ratio.
n­1
a = a (r)
1
n a1 = first number r = common ratio
Nov 26­9:35 AM
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10.6 Geometric Sequences.notebook
February 18, 2016
Writing a Recursive Formula for a Geometric Sequence:
1. Determine that the sequence is geometric.
2. Identify the common ratio.
3. Create a recursive formula using the first term in the sequence and the common ratio.
Nov 26­9:35 AM
Nov 26­9:35 AM
Example 4: Suppose you want to reduce a copy of a photograph. The original length of the photograph is 10 in. The smallest size the copier can make is 64% of the original.
Example 4: Suppose you want to reduce a copy of a photograph. The original length of the photograph is 10 in. The smallest size the copier can make is 64% of the original.
a) Write a sequence of numbers that represents the decrease in photo size.
d) Write a recursive formula to represent the situation.
b) What is the common ratio?
e) Use the explicit formula to find the photograph size after five reductions. c) Write an explicit formula to represent the situation.
Nov 26­9:35 AM
Example 5: A superball is dropped from a height of 5 meters. Each bounce only reaches 50% of the height of the previous bounce. a) Write an explicit formula for the nth term of the sequence that represents the height of the ball after each bounce.
b) Draw a graph to represent the
height of the ball after each bounce.
Nov 26­9:35 AM
Add at the bottom of notes
Using Explicit
an=3(­2)n­1
Find first 3 terms
Using Recursive
a1= ­5
an=3(an­1)
Find next 3 terms
c) What is the domain of this function? Nov 26­9:35 AM
Nov 26­9:35 AM
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