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

Oct 15, 2016

For problems like these, we have to ask ourselves "How many times do I have to add the common difference, $d$, to the first term to get the last term?".

To answer, put a "+d" between -8 and the first space, between the first space and the second space, continuing until you add a d between the last space and the $7$.

In the end, you should have $5$ d's.

We can set up the following equation:

$- 8 + 5 d = 7$

$5 d = 15$

$d = 3$

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

$m = \frac{- 8 + - 5 + - 2 + 1 + 4 + 7}{6}$

$m = - \frac{3}{6}$

$m = - \frac{1}{2}$

Hence, the mean of the numbers in the sequence is $- \frac{1}{2}$.

Hopefully this helps!