Arithmetic and 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.

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CCSS.HSF.BF.A.2

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What is a geometric sequence?

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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.

Tags

CCSS.HSF.BF.A.2

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What is the common difference in an arithmetic sequence?

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The common difference is the constant amount that is added to each term to get the next term in an arithmetic sequence.

Tags

CCSS.HSF.BF.A.2

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

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The nth term (a_n) can be calculated using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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 calculated using the formula: 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

Front

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

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The common ratio (r) can be found by dividing 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 5th term in the arithmetic sequence: 2, 5, 8, 11, ...?

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The 5th term is 14.

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CCSS.HSF.BF.A.2

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What is the 4th term in the geometric sequence: 3, 6, 12, 24, ...?

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The 4th term is 48.

Tags

CCSS.HSF.BF.A.2

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Is the sequence 4, 8, 12, 16 an arithmetic sequence?

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Yes, it is an arithmetic sequence with a common difference of 4.

Tags

CCSS.HSF.BF.A.2

Front

Is the sequence 2, 6, 18, 54 a geometric sequence?

Back

Yes, it is a geometric sequence with a common ratio of 3.

Tags

CCSS.HSF.BF.A.2