Find the 3 arithmetic means between 19 and 52.

Question

Find the 3 arithmetic means between 19 and 52.

Answer 1

Arithmetic means are the numbers that would be part of an arithmetic sequence where 19 is the 1st term and 52 is the 5th term (in this case) - notice that gives tree numbers in the sequence between the two. Like this:

So:

19 + x + x + x + x = 52

19 + 4x = 52

4x = 52 - 19

4x = 33

x = 33/4 = 8.25

So the 1st arithmetic mean is 19 + 8.25 = 27.25

The 2nd arithmetic mean is 27.25 + 8.25 = 35.5

The 3rd arithmetic mean is 35.5 + 8.25 = 43.75

And then we double check things by adding 43.75 + 8.25 and we do indeed get 52