Arithmetic Sequences

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?

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The common difference is the fixed amount that each term increases or decreases by in an arithmetic sequence.

Front

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

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

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What is a recursive formula for an arithmetic sequence?

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A recursive formula defines each term based on the previous term, typically written as: a(n) = a(n - 1) + d.

Front

Find the 10th term of the arithmetic sequence: 3, 7, 11, 15, ...

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The 10th term is 39.

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What is the explicit formula for the arithmetic sequence: 5, 10, 15, ...?

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The explicit formula is a(n) = 5 + (n - 1)5.

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If the first term of an arithmetic sequence is 2 and the common difference is 3, what is the 5th term?

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The 5th term is 14.

Front

What are the next two terms in the sequence: 4, 9, 14, 19?

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The next two terms are 24 and 29.

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How do you determine if a sequence is arithmetic?

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A sequence is arithmetic if the difference between consecutive terms is constant.

Front

What is the common difference of the sequence: 10, 15, 20, 25?

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The common difference is 5.