Geometric Sequence

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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

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What is the common ratio in a geometric sequence?

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

Tags

CCSS.HSF.BF.A.2

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

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

Tags

CCSS.HSF.BF.A.2

Front

What is the explicit formula for a geometric sequence?

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The explicit formula for a geometric sequence is a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

Tags

CCSS.HSF.BF.A.2

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What is the first term of the geometric sequence 3, -12, 48, -192, ...?

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The first term (a_1) is 3.

Tags

CCSS.HSF.BF.A.2

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What is the common ratio of the sequence 3, -12, 48, -192, ...?

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The common ratio (r) is -4.

Tags

CCSS.HSF.BF.A.2

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How do you determine if a sequence is geometric?

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

Tags

CCSS.HSF.BF.A.2

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What is the 9th term of a geometric sequence with a first term of 3 and a common ratio of 2?

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The 9th term is 768.

Tags

CCSS.HSF.BF.A.2

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If the first term of a geometric sequence is 5 and the common ratio is 3, what is the 4th term?

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The 4th term is 135.

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).

Tags

CCSS.HSF.BF.A.2