Practice: Arithmetic and Geometric Sequences

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What is an arithmetic sequence?

Back

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?

Back

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 nth term of an arithmetic sequence?

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The nth term (a_n) 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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How do you find the nth term of a geometric sequence?

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The nth term (a_n) 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 the common difference in the sequence: 3, 7, 11, 15...?

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The common difference is 4.

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What is the common ratio in the sequence: 2, 6, 18, 54...?

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The common ratio is 3.

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If the first term of an arithmetic sequence is 5 and the common difference is 2, what is the 10th term?

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The 10th term is 23.

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If the first term of a geometric sequence is 4 and the common ratio is 2, what is the 5th term?

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The 5th term is 64.

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

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The sum (S_n) of the first n terms of an arithmetic sequence is given by: S_n = n/2 * (a_1 + a_n), where a_n is the nth term.

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

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The sum (S_n) of the first n terms of a geometric sequence is given by: S_n = a_1 * (1 - r^n) / (1 - r), where r is the common ratio.