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 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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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 term that follows it. For example, in the sequence 2, 5, 8, the common difference is 5 - 2 = 3.

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

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The common ratio can be found by dividing any term by the previous term. For example, in the sequence 3, 9, 27, the common ratio is 9 / 3 = 3.

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What is the formula for 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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What is the formula for 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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Determine if the sequence 2, 4, 8, 16 is arithmetic, geometric, or neither.

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The sequence is geometric because each term is multiplied by 2 to get the next term.

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What is the common difference in the sequence 5, 10, 15, 20?

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The common difference is 5.

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What are the next two terms in the arithmetic sequence 12, 15, 18, ...?

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The next two terms are 21, 24.

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What are the next two terms in the geometric sequence 3, 6, 12, ...?

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The next two terms are 24, 48.