Arithmetic vs. Geometric

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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, in the sequence 2, 5, 8, 11, the common difference is 3.

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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, in the sequence 3, 6, 12, 24, the common ratio is 2.

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How do you identify an arithmetic sequence?

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To identify an arithmetic sequence, check if the difference between consecutive terms is the same. If it is, the sequence is arithmetic.

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How do you identify a geometric sequence?

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To identify a geometric sequence, check if the ratio of consecutive terms is constant. If it is, the sequence is geometric.

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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 and d is the common difference.

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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 and r is the common ratio.

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What is a common difference in an arithmetic sequence?

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The common difference is the fixed amount that each term increases or decreases by in an arithmetic sequence. For example, in the sequence 4, 7, 10, the common difference is 3.

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What is a common ratio in a geometric sequence?

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The common ratio is the fixed factor by which each term is multiplied to get the next term in a geometric sequence. For example, in the sequence 5, 15, 45, the common ratio is 3.

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What is a recursive rule for an arithmetic sequence?

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A recursive rule for an arithmetic sequence defines each term based on the previous term. For example, if the first term is 5 and the common difference is 2, the rule is: Next = Prev + 2.

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What is a recursive rule for a geometric sequence?

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A recursive rule for a geometric sequence defines each term based on the previous term. For example, if the first term is 3 and the common ratio is 2, the rule is: Next = Prev * 2.