Alg 3 - Arithmetic Series

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What is an arithmetic series?

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An arithmetic series is the sum of the terms of an arithmetic sequence, where each term after the first is obtained by adding a constant difference to the previous term.

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

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The formula is S_n = n/2 * (a_1 + a_n), where S_n is the sum, n is the number of terms, a_1 is the first term, and a_n is the last term.

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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.

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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 each term increases or decreases by in an arithmetic sequence.

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

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The 10th term is 32.

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What is the sum of the first 10 even integers?

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The sum is 110.

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How do you calculate the sum of an infinite arithmetic series?

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An infinite arithmetic series does not converge; it diverges unless the common difference is zero.

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What is the significance of the first term in an arithmetic series?

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The first term is crucial as it serves as the starting point for calculating subsequent terms and the overall sum.

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What is the sum of the series 1 + 3 + 5 + ... + 99?

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The sum is 2500.

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How do you determine the number of terms in an arithmetic series?

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