Arithmetic sequence

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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 constant amount that is added to each term to get the next term in the sequence.

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Write the explicit formula for an arithmetic sequence.

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The explicit formula for an arithmetic sequence is a_n = a_1 + (n-1)d, where a_1 is the first term and d is the common difference.

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Given the sequence: 10, 15, 20, 25,... What is the common difference?

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The common difference is 5.

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If the first term of an arithmetic sequence is 3 and the common difference is 4, what is the 5th term?

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The 5th term is 3 + (5-1)4 = 3 + 16 = 19.

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

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To find the nth term, use the formula a_n = a_1 + (n-1)d.

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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 2 + (10-1)3 = 2 + 27 = 29.

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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 is S_n = n/2 * (a_1 + a_n), or S_n = n/2 * (2a_1 + (n-1)d).

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If the 4th term of an arithmetic sequence is 12 and the common difference is 2, what is the first term?

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The first term is 12 - 3*2 = 6.

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What is the relationship between the terms in an arithmetic sequence?

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Each term is obtained by adding the common difference to the previous term.