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

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What is the formula for the nth term of a geometric sequence?

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The nth term of a geometric sequence 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.

Tags

CCSS.HSF.BF.A.2

Front

What does the common ratio represent in a geometric sequence?

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The common ratio is the factor by which each term in the sequence is multiplied to get the next term.

Tags

CCSS.HSF.BF.A.2

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

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

Tags

CCSS.HSF.BF.A.2

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What is the first term of a geometric sequence denoted as?

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The first term of a geometric sequence is denoted as a_1.

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 is a recursive formula for a geometric sequence?

Back

A recursive formula for a geometric sequence is a_n = r * a_(n-1), where r is the common ratio.

Tags

CCSS.HSF.BF.A.2

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What is the 3rd term of the geometric sequence 2, 6, 18, ...?

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The 3rd term is 18.

Tags

CCSS.HSF.BF.A.2

Front

What is the 5th term of the geometric sequence 4, 12, 36, ...?

Back

The 5th term is 4 * 3^(5-1) = 4 * 81 = 324.

Tags

CCSS.HSF.BF.A.2

Front

If a geometric sequence has a common ratio of 1/2, what happens to the terms?

Back

The terms of the sequence decrease by half with each subsequent term.

Tags

CCSS.HSF.BF.A.2