Provide an example of an arithmetic series which totals zero. Using complete sentences, explain how you created the example.
how about
-5 -4 -3 -2 - 1 +0 +1 +2 +3 +5+4 +5 ?
To create an arithmetic series that totals zero, you need to find a sequence of numbers where the sum of all the terms is equal to zero. For this, you can use the formula for the sum of an arithmetic series, which is given by:
Sum = (n/2)(a + l)
Where:
- Sum is the total sum of the series,
- n is the number of terms in the series,
- a is the first term of the series, and
- l is the last term of the series.
In this case, since we want the sum to be zero, we can set the equation:
0 = (n/2)(a + l)
To simplify this equation, we can divide both sides by n/2:
0 = a + l
This means that the first term, a, must be the negative of the last term, l, in order for the sum to be zero.
So, an example of an arithmetic series that totals zero could be:
-3, -1, 1, 3, 5
In this example, the first term, -3, is the negative of the last term, 5, which satisfies the condition for a sum of zero. By adding up all the terms in the series, we will get a sum of zero:
-3 + (-1) + 1 + 3 + 5 = 0.