Arithmetic & 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.

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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 calculated 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 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 nth term of a geometric sequence can be calculated 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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How do you find the common difference in an arithmetic sequence?

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The common difference in an arithmetic sequence is found by subtracting any term from the subsequent term: 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 in a geometric sequence is found by dividing any term by the previous term: r = a_(n+1) / a_n.

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What is the sum of the first n terms of an arithmetic sequence?

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The sum of the first n terms of an arithmetic sequence can be calculated using the formula: S_n = n/2 * (a_1 + a_n), where S_n is the sum, a_1 is the first term, and a_n is the nth term.

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What is the sum of the first n terms of a geometric sequence?

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The sum of the first n terms of a geometric sequence can be calculated using the formula: S_n = a_1 * (1 - r^n) / (1 - r), where S_n is the sum, a_1 is the first term, and r is the common ratio.

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How do you determine if a sequence is arithmetic?

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A sequence is arithmetic if the difference between consecutive terms is constant.

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How do you determine if a sequence is geometric?

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A sequence is geometric if the ratio of consecutive terms is constant.