Arithmetic Sequence: Mean

How to find the arithmetic means of an arithmetic sequence: definition, 1 example, and its solution.

Definition

Definition

The arithmetic means are the terms
that form an arithmetic sequence
with the first and the last term.

In this figure,
a1, the blanks, and a4
form an arithmetic sequence.
Then the blanks are the arithmetic means.

Example

Example

Solution

It says
find the three arithmetic means
between 7 and 23.

So write 7, three blanks (the arithmetic means), and 23.

Write the common difference +d
between the terms.

23 is found by
adding the first term 7
and d 4 times.

So 23 = 7 + 4d.

Write 7 + 4d = 23.

Move 7 to the right side.

Then 4d = 16.

Divide both sides by 4.

Then d = 4.

a = 7
d = 4

Then find the three arithmetic means
by adding d = 4.

7 + 4 = 11

This 11 is the first arithmetic mean.

11 + 4 = 15

This 15 is the second arithmetic mean.

15 + 4 = 19

This 19 is the third arithmetic mean.

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

So
11, 15, 19
is the answer.