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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. This difference is called the common difference (d).

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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 (r).

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CCSS.HSF.BF.A.2

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How do you find the common difference in an arithmetic sequence?

Back

To find the common difference (d), subtract any term from the subsequent term: d = a(n+1) - a(n).

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CCSS.HSF.BF.A.2

Front

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

Back

To find the common ratio (r), 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 next term in the arithmetic sequence: 2, 5, 8, 11...?

Back

The next term is 14 (common difference d = 3).

Tags

CCSS.HSF.BF.A.2

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What is the next term in the geometric sequence: 3, 6, 12, 24...?

Back

The next term is 48 (common ratio r = 2).

Tags

CCSS.HSF.BF.A.2

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Identify the type of sequence: 4, 8, 12, 16...

Back

This is an arithmetic sequence with a common difference d = 4.

Tags

CCSS.HSF.BF.A.2

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Identify the type of sequence: 5, 10, 20, 40...

Back

This is a geometric sequence with a common ratio r = 2.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for the nth term of an arithmetic sequence?

Back

The nth term (a_n) can be found using the formula: a_n = a_1 + (n-1)d.

Tags

CCSS.HSF.BF.A.2

Front

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

Back

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

Tags

CCSS.HSF.BF.A.2