Geometric Sequence and Exponential Functions
Presentation
•
Mathematics
•
9th - 11th Grade
•
Hard
Joseph Anderson
FREE Resource
5 Slides • 6 Questions
1
Definition: A sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Example: 5, 10, 20, 40, 80 is a geometric sequence because you multiply by 2 to find the next term. The common ratio is 2.
Geometric Sequences
2
Open Ended
Is this a geometric sequence? 2,4,8,16,32....
3
4
Multiple Choice
Is this a geometric sequence? 1,3,9,27....
Yes, you MULTIPLY by 3 each time.
No, because you are adding each time.
Yes, you ADD by 3 each time.
5
Multiple Choice
Is this a geometric sequence? 10, 12, 14, 16, 18...
Yes, you multiply by 2 each time.
No, this sequence is actually arithmetic because you add by 2 each time.
6
Multiple Choice
What is the common ratio (the number you multiply by each time) of this geometric sequence? 5, 20, 80, 320...
2
6
4
20
7
8
Multiple Choice
What is the common ratio (the number you multiply by each time) of this geometric sequence? 100, 50, 25, 12.5...
2
1/2
1/4
9
These sequences are exponential (like the graph shown) because they grow fast (since you are multiplying each time).
Geometric Sequence Graphs
10
Graph can also decrease exponentially if you multiply by a fraction.
Common ratio is 1/2 for this graph.
Other Geometric Sequence Graphs
11
Multiple Choice
What is the common ratio shown for this geometric sequence (exponential graph)? Hint: Sequence given by y-values on graph.
2 because you multiply each term by 2 to get next term.
4 because you multiply each term by 4 to get next term.
Definition: A sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
Example: 5, 10, 20, 40, 80 is a geometric sequence because you multiply by 2 to find the next term. The common ratio is 2.
Geometric Sequences
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