Question

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

Answer 1

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 + 5d = 7`

`5d = 15`

`d = 3`

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

`m = (-8 + -5 + -2 + 1 + 4 + 7)/6`

`m = -3/6`

`m = -1/2`

Hence, the mean of the numbers in the sequence is `-1/2`.

Hopefully this helps!