2C: Arithmetic Series

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.

Front

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.

Front

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.

Front

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

Back

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

Front

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.

Front

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.