2C: Arithmetic Series

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What is an arithmetic series?

Back

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 of the first n terms, a_1 is the first term, a_n is the nth term, and n is the number of terms.

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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 can be found using the formula a_n = a_1 + (n-1)d. Here, a_10 = 5 + (10-1) * 3 = 32.

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Calculate the sum of the first 10 terms of the arithmetic series: 2, 5, 8, ...

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The first term a_1 = 2, the common difference d = 3, and the 10th term a_10 = 2 + (10-1) * 3 = 29. Using the formula S_n = n/2 * (a_1 + a_n), S_10 = 10/2 * (2 + 29) = 155.

Front

What is the common difference in the arithmetic series: -8, -10, -12, -14, -16?

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The common difference d is -2, calculated as -10 - (-8) = -2.

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How do you express the sum of an arithmetic series using sigma notation?

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The sum of an arithmetic series can be expressed in sigma notation as S = Σ (a_1 + (n-1)d) for n = 1 to N, where N is the number of terms.

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What is the sum of the arithmetic series: 1, 3, 5, ..., 99?

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This series has 50 terms. Using the formula S_n = n/2 * (a_1 + a_n), S_50 = 50/2 * (1 + 99) = 2500.

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If the sum of an arithmetic series is 136 and the first term is 8, what is the last term if there are 10 terms?

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Using S_n = n/2 * (a_1 + a_n), we have 136 = 10/2 * (8 + a_n). Solving gives a_n = 24.

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What is the 5th term of the arithmetic series: 4, 7, 10, ...?

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The 5th term can be calculated as a_5 = a_1 + (5-1)d = 4 + (4 * 3) = 16.

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Find the sum of the arithmetic series: 10, 20, 30, ..., 100.

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This series has 10 terms. Using S_n = n/2 * (a_1 + a_n), S_10 = 10/2 * (10 + 100) = 550.