Arithmetic Sequences Quick Check

Front

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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What is the common difference in an arithmetic sequence?

Back

The common difference (d) is the constant amount that each term increases or decreases by in an arithmetic sequence.

Front

How do you find the explicit formula for an arithmetic sequence?

Back

The explicit formula for an arithmetic sequence can be written as a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

Front

What is the explicit formula for the sequence: 2, 8, 14, ...?

Back

a_n = 6n - 4.

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What is the explicit formula for the sequence: 25, 21, 17, 13,...?

Back

a_n = -4n + 29.

Front

How do you identify the common difference in a sequence?

Back

To find the common difference, subtract the first term from the second term (d = a_2 - a_1).

Front

What is the common difference in the sequence: 97, 86, 75, 64, ...?

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d = -11.

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

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Use the formula a_n = a_1 + (n-1)d to calculate the nth term.

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What is the 32nd term of the sequence: 9, 4, -1, -6, -11, ...?

Back

-146.

Front

What is a recursive rule in an arithmetic sequence?

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A recursive rule defines each term based on the previous term, typically in the form a_n = a_(n-1) + d.