Exponential Functions and Geometric Sequences

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.

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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

Open Ended

Is this a geometric sequence? 2,4,8,16,32....

Yes!

The sequence given by 2,4,8,16,32.... is geometric because you multiply by 2 each time to find the next term.

The common ratio is 2.

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.

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.

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

The common ratio of the geometric sequence given by 40,20,10, 5 .... is 1/2 because you multiply by one half (or 0.5) each time.

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

These sequences are exponential (like the graph shown) because they grow fast (since you are multiplying each time).

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​Geometric Sequence Graphs

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Graph can also decrease exponentially if you multiply by a fraction.​​

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Common ratio is 1/2 for this graph.​

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​Other Geometric Sequence Graphs

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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.