Arithmetic vs Geometric Sequences

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What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

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CCSS.HSF.BF.A.2

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. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

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CCSS.HSF.BF.A.2

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How do you find the nth term of an arithmetic sequence?

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

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CCSS.HSF.BF.A.2

Front

How do you find the nth term of a geometric sequence?

Back

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.

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CCSS.HSF.BF.A.2

Front

What is the common difference in an arithmetic sequence?

Back

The common difference in an arithmetic sequence is the constant amount that each term increases or decreases by. It is calculated by subtracting any term from the subsequent term.

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CCSS.HSF.BF.A.2

Front

What is the common ratio in a geometric sequence?

Back

The common ratio in a geometric sequence is the constant factor by which each term is multiplied to get the next term. It is calculated by dividing any term by the previous term.

Tags

CCSS.HSF.BF.A.2

Front

Identify if the sequence 5, 10, 15, 20 is arithmetic or geometric.

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The sequence 5, 10, 15, 20 is an arithmetic sequence with a common difference of 5.

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CCSS.HSF.BF.A.2

Front

Identify if the sequence 2, 6, 18, 54 is arithmetic or geometric.

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The sequence 2, 6, 18, 54 is a geometric sequence with a common ratio of 3.

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CCSS.HSF.BF.A.2

Front

What is the 9th term of the arithmetic sequence 6, 11, 16, 21?

Back

The 9th term is 46.

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CCSS.HSF.BF.A.2

Front

What is the common difference of the sequence 97, 86, 75, 64?

Back

The common difference is -11.

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CCSS.HSF.BF.A.2