Geometric Sequence

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

What is the common ratio in a geometric sequence?

Back

The common ratio (r) is the factor by which we multiply each term to get the next term in the sequence.

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CCSS.HSF.BF.A.2

Front

How do you find the next term in a geometric sequence?

Back

To find the next term, multiply the last known term by the common ratio.

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CCSS.HSF.BF.A.2

Front

What is the explicit formula for a geometric sequence?

Back

The explicit formula is given by a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number.

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CCSS.HSF.BF.A.2

Front

Given the sequence 512, 256, 128, what are the next three terms?

Back

64, 32, 16.

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CCSS.HSF.BF.A.2

Front

Is the sequence -432, 72, -12, 2 geometric?

Back

Yes, it is geometric because each term is obtained by multiplying the previous term by a common ratio.

Tags

CCSS.HSF.BF.A.2

Front

What is the common ratio of the sequence 10, 40, 160, 640?

Back

The common ratio is 4.

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CCSS.HSF.BF.A.2

Front

Write the explicit formula for the geometric sequence 3, -12, 48, -192.

Back

a_n = 3(-4)^(n-1).

Tags

CCSS.HSF.BF.A.2

Front

If a_n = 10(2)^(n-1), what is the common ratio?

Back

The common ratio is 2.

Tags

CCSS.HSF.BF.A.2

Front

How do you determine if a sequence is geometric?

Back

A sequence is geometric if the ratio of consecutive terms is constant.

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CCSS.HSF.BF.A.2