Arithmetic vs 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. For example, 2, 4, 6, 8 is an arithmetic sequence with a common difference of 2.

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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. For example, 3, 6, 12, 24 is a geometric sequence with a common ratio of 2.

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

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The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n-1)d, where a_1 is the first term, d is the common difference, and n is the term number.

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How do you find the nth term of a geometric sequence?

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

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What is the common difference in an arithmetic sequence?

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The common difference in an arithmetic sequence is the constant amount that each term increases or decreases by. It is calculated by subtracting any term from the subsequent term.

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What is the common ratio in a geometric sequence?

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The common ratio in a geometric sequence is the constant factor by which each term is multiplied to get the next term. It is calculated by dividing any term by the previous term.

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Identify if the sequence 5, 10, 15, 20 is arithmetic or geometric.

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The sequence 5, 10, 15, 20 is an arithmetic sequence with a common difference of 5.

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Identify if the sequence 2, 6, 18, 54 is arithmetic or geometric.

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The sequence 2, 6, 18, 54 is a geometric sequence with a common ratio of 3.

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What is the 9th term of the arithmetic sequence 6, 11, 16, 21?

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The 9th term is 46.

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What is the common difference of the sequence 97, 86, 75, 64?

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The common difference is -11.