Pearson Algebra 2 Common Core, 2011
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Pearson Algebra 2 Common Core, 2011 View details
4. Arithmetic Series
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Exercise 7 Page 591

We will investigate whether it is possible to have more than one arithmetic series with four terms whose sum is Let's first recall the definition of an arithmetic series.

The sum of the terms in an arithmetic sequence is called an arithmetic series.

According to this definition, it looks like we should focus on the summation of the terms. Let's now recall the formula for the sum of an arithmetic series.
By substituting the given values and in the above formula, we can find a condition that the desired arithmetic series must satisfy.
With this information, we can conclude that any arithmetic series with terms in which the sum of the first and fourth terms is will have a sum of Let's write three examples. Recall that the difference between consecutive terms must be constant!
The above are examples of arithmetic series because they have a constant common difference. Moreover, note that the sum of the four terms of each series is Also, note that the sum of the first and fourth terms is