Explicit Formulas for Sequences

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What is an explicit formula for a sequence?

Back

An explicit formula for a sequence is a formula that allows you to calculate the nth term of the sequence directly, without needing to know the previous terms.

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How do you identify if a sequence is arithmetic?

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

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What is the explicit formula for the arithmetic sequence 15, 22, 29, 36, 43, ...?

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What is the common difference in the sequence 15, 22, 29, 36, 43, ...?

Back

The common difference is 7.

Front

What is the explicit formula for the sequence -3, -33, -63, -93, ...?

Back

Front

How do you find the nth term of a sequence given its explicit formula?

Back

Substitute n into the explicit formula to calculate the nth term.

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Back

The 15th term is 5.

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The first four terms are 3, 8, 13, 18.

Front

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

Back

Front

What does the term 'common difference' mean in an arithmetic sequence?

Back

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