Front

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.

Front

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

Back

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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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.

Front

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

Back

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

Front

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

Back

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

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How do you represent an arithmetic series in sigma notation?

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An arithmetic series can be represented in sigma notation as Σ (a_1 + (n-1)d) from n=1 to N, where a_1 is the first term, d is the common difference, and N is the number of terms.

Front

Find the sum of the arithmetic series: 1, 3, 5, ..., 19.

Back

The series has 10 terms. S_10 = 10/2 * (1 + 19) = 100.

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

Back

The 5th term is a_5 = 4 + (5-1)3 = 16.

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If the sum of an arithmetic series is 50 and there are 5 terms, what is the average of the terms?

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The average of the terms is the sum divided by the number of terms: 50/5 = 10.

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What is the first term of an arithmetic series if the 7th term is 20 and the common difference is 2?

Back

Using the formula a_n = a_1 + (n-1)d, we have 20 = a_1 + 6*2. Thus, a_1 = 20 - 12 = 8.