Question

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Provide an example of an arithmetic series which totals zero. Using complete sentences, explain how you created the example.

Answer 1

In an arithmetic series you get the next term by adding the same number to the current term each time. Or you get the previous term by subtracting the same number from the current term each time. The "same number" is called the common difference.

Let us choose a common difference of 5.
Start with the current term 0. Add 5 to get the next term. 0 + 5 = 5
Subtract 5 to get the previous term 0 - 5 = -5
So we now have three terms in the arithmetic sequence: -5, 0, +5
You add them all up and you get the sum to be 0.
You can keep going to get a few more terms: ..., -15, -10, -5, 0, 5, 10, 15, ....