Arithmetic Sequence and Series

Front

What is an arithmetic sequence?

Back

An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference is called the common difference.

Front

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

Back

The common difference (d) can be found by subtracting any term from the subsequent term: d = a_{n+1} - a_n.

Front

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

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The explicit formula is given by: a_n = a_1 + (n - 1)d, where a_1 is the first term and d is the common difference.

Front

What is the recursive formula for an arithmetic sequence?

Back

The recursive formula is given by: a_n = a_{n-1} + d, where d is the common difference.

Front

Given the explicit rule a_n = 2n + 5, what are the first four terms of the sequence?

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The first four terms are 7, 9, 11, 13.

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How do you identify the common difference in a sequence?

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To identify the common difference, subtract the first term from the second term. For example, in the sequence 97, 86, 75, 64, the common difference is -11.

Front

What is the recursive rule for the sequence 17, 10, 3, -4, -11?

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The recursive rule is a_n = a_{n-1} - 7.

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What is the recursive rule for the sequence -5, -1, 3, 7, 11?

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The recursive rule is a_n = a_{n-1} + 4.

Front

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

Back

To find the nth term, use the formula: a_n = a_1 + (n - 1)d.

Front

If a_1 = 5 and d = 0.5, what is the 25th term of the sequence?

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The 25th term is 17.