7.2 Geometric Sequences
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7.2 Geometric Sequences
A geometric sequence is an ordered list where new terms are generated by multiplying the previous term by a non­zero constant. This constant is called the common ratio (r).
Ex: 1) 1, 2, 4, 8, 16, ...
2) 6250, 1250, 250, 50, 10, ...
Can you ...
­ predict the next term?
­ create a general term?
3) 32, ­48, 72, ­108, 162
The General Term of a Geometric Sequence
Investigation #1
1.
2.
3. Complete this table of values to create a geometric sequence.
Use your table of values to graph this function.
Suggest an equation that could be used to model this sequence.
n
tn
1
3
2
6
3
4
5
6
Hmwk ­ P.430 #1, 2ac, 3, 6ace, 7, 11­14
7.2 Geometric Sequences
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Investigation #2
Now consider this sequence:
a, ar, ar2, ar3, ar4, ...
Why is this a geometric sequence?
The General Term of a Geometric Sequence:
tn = arn­1
Examples
1. State the general term of:
a) 2, 6, 18, 54, 162, ...
b) 5, ­10, 20, ­40, 80, ...
c) 2187, 729, 243, 81, ...
2. Determine t10 for: 4096, ­2048, 1024, ­512, 256, ...
Hmwk ­ P.430 #1, 2ac, 3, 6ace, 7, 11­14
tn = arn­1
7.2 Geometric Sequences
3. In a certain geometric sequence, t2 = 12 and t7 = 2916.
Determine the general term of this sequence.
What is a "recursive" formula?
In a recursive formula, the general term defines a sequence in terms of its previous terms. We would state a starting value for t1 and then create a rule that define the next term (tn ) using the previous term (tn­1 ).
Ex1:
2, 6, 18, 54, ...
Ex2:
5, 10, 20, 40, ...
Ex3:
4,­20,100,­500, ...
Ex4:
2, 5, 8, 11, 14, ...
Hmwk ­ P.430 #1, 2ac, 3, 6ace, 7, 11­14
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