Arithmetic 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 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.

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How do you find the nth term of an arithmetic sequence?

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The nth term 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.

Front

What is the first term (a_1) in the sequence 5, 10, 15, 20,...?

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The first term (a_1) is 5.

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What is the common difference of the sequence 3, 7, 11, 15,...?

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The common difference is 4.

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What is the 10th term of the arithmetic sequence 2, 5, 8, 11,...?

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The 10th term is 29.

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Which of the following sequences is an arithmetic sequence: 1, 3, 5, 7 or 2, 4, 8, 16?

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1, 3, 5, 7 is an arithmetic sequence.

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

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The 5th term is 2.

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

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

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What is the common difference of the sequence 12, 18, 24, 30,...?

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The common difference is 6.