# How do you find the arithmetic means of the sequence -8, __, __, __, __, 7?

We can set up the following equation:

I'm assuming that by arithmetic means you mean average, or mean, of the whole sequence.

Hopefully this helps!

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To find the arithmetic mean of a sequence, you sum all the numbers in the sequence and then divide by the total count of numbers. In this case, we have -8 and 7, and four missing numbers in between. Since the sequence is evenly spaced, we can calculate the missing numbers by finding the common difference (d) and using it to fill in the sequence.

First, find the common difference (d) using the formula: [ d = \frac{{\text{{Last term}} - \text{{First term}}}}{{\text{{Number of terms}} - 1}} ]

[ d = \frac{{7 - (-8)}}{{6}} = \frac{{15}}{{6}} = \frac{5}{2} ]

Now, fill in the missing numbers using the common difference: [ -8, -8 + \frac{5}{2}, -8 + 2\left(\frac{5}{2}\right), -8 + 3\left(\frac{5}{2}\right), -8 + 4\left(\frac{5}{2}\right), 7 ]

[ -8, -8 + \frac{5}{2}, -8 + 2\left(\frac{5}{2}\right), -8 + 3\left(\frac{5}{2}\right), -8 + 4\left(\frac{5}{2}\right), 7 ]

[ -8, -8 + \frac{5}{2}, -8 + 5, -8 + \frac{15}{2}, -8 + 10, 7 ]

[ -8, -8 + \frac{5}{2}, -3, -8 + \frac{15}{2}, 2, 7 ]

Now, sum all the numbers and divide by the total count of numbers: [ \frac{{-8 + (-3) + (-8 + \frac{15}{2}) + 2 + 7}}{6} ]

[ \frac{{-8 - 3 - 8 + \frac{15}{2} + 2 + 7}}{6} ]

[ \frac{{-12 + \frac{15}{2} + 6}}{6} ]

[ \frac{{-12 + 7.5 + 6}}{6} ]

[ \frac{{1.5}}{6} ]

[ \frac{{3}}{12} ]

[ \frac{1}{4} ]

So, the arithmetic mean of the sequence is ( \frac{1}{4} ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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