Arithmetic Sequence 910

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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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How do you find 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, n is the term number, and d is the common difference.

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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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If the first term of an arithmetic sequence is 5 and the common difference is 3, what is the 10th term?

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The 10th term is 32, calculated as a_10 = 5 + (10-1)3 = 5 + 27 = 32.

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How can you determine the number of terms in an arithmetic sequence?

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You can determine the number of terms by rearranging the nth term formula: n = (a_n - a_1) / d + 1.

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What is the explicit formula for the arithmetic sequence 10, 15, 20, 25...?

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The explicit formula is a_n = 10 + (n-1)5.

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How do you calculate the sum of the first n terms of an arithmetic sequence?

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The sum of the first n terms can be calculated using the formula: S_n = n/2 * (a_1 + a_n), or S_n = n/2 * (2a_1 + (n-1)d).

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In the sequence 25, 21, 17, 13,... what is the common difference?

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The common difference is -4, as each term decreases by 4.

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What is the 41st term of the sequence 230, 226, 222, 218...?

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The 41st term is 70, calculated using the nth term formula.

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How do you find the total number of terms in a sequence given the first term, common difference, and last term?

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Use the formula n = (last term - first term) / common difference + 1.