# Arithmetic Sequence: Mean

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

## Definition

The arithmetic means are the terms

that form an arithmetic sequence

with the first and the last term.

In this figure,

a_{1}, the blanks, and a_{4}

form an arithmetic sequence.

Then the blanks are the arithmetic means.

## ExampleThree Arithmetic Means, 7 and 23

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.