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?

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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 term that precedes it. For example, in the sequence 3, 6, 12, the common ratio is 6 / 3 = 2.

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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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If the first term of a geometric sequence is 2 and the common ratio is 3, what is the 4th term?

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The 4th term is 2 * 3^(4-1) = 2 * 27 = 54.

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What is the common ratio of the sequence 5, 15, 45, 135?

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The common ratio is 15 / 5 = 3.

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If an arithmetic sequence starts with 10 and has a common difference of 4, what is the 5th term?

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The 5th term is 10 + (5-1) * 4 = 10 + 16 = 26.

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What is the next term in the sequence 1, 4, 7, 10?

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The next term is 10 + 3 = 13.