Geometric Sequences

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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?

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The common ratio 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

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

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

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CCSS.HSF.BF.A.2

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What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence 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.

Tags

CCSS.HSF.BF.A.2

Front

Given the sequence 4, 16, 64, what is the next term?

Back

The next term is 256.

Tags

CCSS.HSF.BF.A.2

Front

Find the common ratio for the sequence 4, -16, 64, -256, ...

Back

The common ratio is -4.

Tags

CCSS.HSF.BF.A.2

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Write the explicit formula for the geometric sequence 7, -7, 7, -7, ...

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The explicit formula is a_n = 7(-1)^(n-1).

Tags

CCSS.HSF.BF.A.2

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Write the explicit formula for the geometric sequence 100, 50, 25, ...

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The explicit formula is a_n = 100(1/2)^(n-1).

Tags

CCSS.HSF.BF.A.2

Front

If the first term of a geometric sequence is 3 and the common ratio is 2, what is the 5th term?

Back

The 5th term is 3 * 2^(5-1) = 48.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula to find the nth term of a geometric sequence?

Back

The nth term can be found using the formula a_n = a_1 * r^(n-1).

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CCSS.HSF.BF.A.2