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

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The common difference can be found by subtracting any term from the subsequent term in the sequence.

Front

What is the explicit formula for an arithmetic sequence?

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The explicit formula for an arithmetic sequence is given by 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 the recursive formula for an arithmetic sequence?

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The recursive formula for an arithmetic sequence is given by a_1 = first term, a_n = a_(n-1) + d.

Front

How do you derive the explicit formula from the first few terms of an arithmetic sequence?

Back

Identify the first term and the common difference, then use the explicit formula a_n = a_1 + (n-1)d.

Front

Given the sequence 3, 7, 11, 15, what is the common difference?

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The common difference is 4.

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If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

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The 10th term is 32.

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

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The 32nd term is -146.

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How can you check if a sequence is arithmetic?

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

Front

What is the formula to 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.