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Geometric Sequences
Lesson Objectives:
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Review Exponent Laws
You should be able to identify if a sequence is geometric
Given a geometric sequence, you should be able to determine “a” and “r’.
You should be able to determine the “nth term” of a geometric sequence
You should be able to apply the “nth term” formula to various problem solving situations
A) Exponent Law Review
36  315 
a 3  a 24 
m7n 5  mn8 
3m8  7m 9 
416  48 
x12  x 4 
a16b9  a 4b3 
24m 26  6m3 
2 
m 
a b 
 3x 
6 3

8 6
6 2 4


7 4

B) Definition of a Geometric Sequence
You have just classified many different sequences. Select two from the group we called Geometric.
Sequence
Calculations
What do I see?
U5

U4
U3

U2
U4

U3
U2

U1
U5

U4
U3

U2
U5

U4
U3

U2
U4

U3
U2

U1
U4

U3
U2

U1
A GEOMETRIC SEQUENCE is a sequence of numbers…
Geometric Sequences
C) The General Term of Nth Term of a Geometric Sequence
Consider the Geometric sequence
Position
of term
“n”
Term Un
1
2
3
4
a
ar
ar2
ar3
8…..
The General term (nth Term) of an Geometric Sequence is:
Un = ____________
15…..
75…..
n
What does the nth term mean?
What can we use it for?
where n is _______________
a is _____________
r is _____________
D) Using the nth Term – In your home groups of 4, select a number 1-4.
Problem 1
Problem 2
Show this Geometric arithmetic?
For the geometric sequence: 5, -10, 20, -40, 80,…..
3, 3.6, 4.32, 5.184,……
Determine a and r, and hence an equation for Un
Determine the common ratio ‘r’.
Problem 3
Problem 4
Determine the first 5 terms of the sequence:
For the geometric sequence: 3, 3.6, 4.32, 5.184,……
Un = -2 . 3n
Determine U13
Geometric Sequences
E) Practice – refer to weebly
F) Applications of Geometric Sequences – Compound Interest
Scenario: If the $5000 is invested for 5 years at 6% interest, compounded yearly. How much will this investment
compound to at the end of this period?
How can geometric sequences help solve this problem
G) Challenge - Use your understanding of nth term to help with these problems.
1.
The terms m + 4, 5m + 4, m + 20 are in geometric sequence. Find the value(s) of ‘m’
2. For a given geometric sequence U1  U 3  40 , and U 2  U 4  96