Question

find the 3 arithmetic means between between 18 and -10

Answer 1

we have the following:

The arithmetic means are the numbers that would be part of an arithmetic sequence where 18 is the first term and -10 is the fifth term (in this case); notice that it gives tree numbers in the sequence between the two. I like this

$18\rightarrow x\rightarrow x\rightarrow x\rightarrow-10$

so:

$\begin{gathered} 18+x+x+x+x=-10 \\ 18+4x=-10 \\ 4x=-10-18 \\ x=-\frac{28}{4} \\ x=-7 \end{gathered}$

therefore,

the 1st arithmetic mean is:

$18-7=11$

the 2nd arithmetic mean is:

$11-7=4$

the 3rd arithmetic mean is:

$4-7=-3$