Arithmetic and Geometric Sequences

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What is an arithmetic sequence?

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

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

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The formula for the nth term (a_n) of an arithmetic sequence is: 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 geometric sequence?

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A geometric sequence is a sequence of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio.

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What is the formula for the nth term of a geometric sequence?

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The formula for the nth term (a_n) of a geometric sequence is: a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.

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

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The common difference (d) in an arithmetic sequence can be found by subtracting any term from the term that follows it: d = a_(n+1) - a_n.

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How do you find the common ratio in a geometric sequence?

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The common ratio (r) in a geometric sequence can be found by dividing any term by the previous term: r = a_(n+1) / a_n.

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What is the 38th term of the sequence: 26, 22, 18, 14, ...?

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The 38th term is -122.

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What is the common ratio of the geometric sequence: 5, 25, 125, 625...?

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The common ratio is 5.

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Identify the common difference in the sequence: 97, 86, 75, 64, ...

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The common difference is -11.

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Which kind of sequence has a common ratio?

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A geometric sequence has a common ratio.