Arithmetic Means

Arithmetic Means

How to find the arithmetic means: example and its solution.

Example

Find the three arithmetic means between 7 and 23.

Arithmetic means are the terms
between the given terms
that form an arithmetic sequence.

To find the three arithmetic means between 7 and 23,
write 7, three blanks, and 23.

These five terms are an arithmetic sequence.

Set the common difference as d.

Then the first blank is 7 + d.
The second blank is 7 + 2d.
The third blank is 7 + 3d.
And 23 is 7 + 4d.

Arithmetic sequences

23 is 7 + 4d.

So 7 + 4d = 23.

Move 7 to the right side.

Then 4d = 16.

Divide both sides by 4.

Then d = 4.

d = 4

To find the values of the blanks,
start from 7
and add +4.

The first blank is, 7 + 4, 11.

The second blank is, 11 + 4, 15.

And the third blank is, 15 + 4, 19.

19 + 4 is 23,
which is the last term.
So you found the right terms.

So the three arithmetic means are
11, 15, and 19.