Geometric Sequences: Find the Common Ratio

Front

What is a geometric sequence?

Back

A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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CCSS.HSF.BF.A.2

Front

How do you find the common ratio in a geometric sequence?

Back

To find the common ratio (r), divide any term in the sequence by the previous term (r = a_n / a_(n-1)).

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CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence -3, 9, -27, 81, ...?

Back

r = -3

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CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence 4, -12, 36, -108, ...?

Back

r = -3

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CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence 1, 3, 9, 27, ...?

Back

r = 3

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CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence -4, -8, -16, -32, ...?

Back

r = 2

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CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence -3, 18, -108, 648, ...?

Back

r = -6

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CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 5 and the common ratio is 2, what is the second term?

Back

The second term is 10 (5 * 2).

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CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 7 and the common ratio is -3, what is the third term?

Back

The third term is 63 (7 * -3 * -3).

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CCSS.HSF.BF.A.2

Front

What happens to the terms of a geometric sequence if the common ratio is between 0 and 1?

Back

The terms will decrease and approach zero.