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 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 nth term of a geometric sequence?

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The nth term can be found using the formula: 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

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What does a_1 represent in a geometric sequence?

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a_1 represents the first term of the geometric sequence.

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 5 * 3^(4-1) = 5 * 27 = 135.

Tags

CCSS.HSF.BF.A.2

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What are the next three terms in the geometric sequence: 2, 6, 18, ...?

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The next three terms are 54, 162, 486.

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 formula for the sum of the first n terms of a geometric sequence?

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The sum S_n of the first n terms is given by S_n = a_1 * (1 - r^n) / (1 - r) for r ≠ 1.

Tags

CCSS.HSA.SSE.B.4

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If a geometric sequence has a common ratio of 1/2 and the first term is 16, what is the 5th term?

Back

The 5th term is 16 * (1/2)^(5-1) = 16 * (1/16) = 1.

Tags

CCSS.HSF.BF.A.2

Front

What is the 3rd term in the geometric sequence: 81, 27, ...?

Back

The 3rd term is 9.

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CCSS.HSF.BF.A.2