We already know that in a** PAN**:

Note that we can write all the terms of a **PAN** in function of and **r**:

Therefore, the general term of **PAN** will be given by the formula:

, no |

- = first term
- = nth term
**r**= reason**no**= number of terms

**Example 1**

Determine the general term of **PA (-19, -15, -11,…)**:

*Resolution*

The general term of **PA (-19, -15, -11,…)** é .

**Example 2**

Determine the 16th term of the **PA (3, 9, 15,…)**:

*Resolution*

Therefore, the 16th term of **PA (3, 9, 15,…)** é **93**.

**Example 3**

Interpolate six arithmetic means between** -8** and** 13**:

*Resolution *

From the statement we have to:

Once reason is found, just interpolate the arithmetic means: **(-8, -5, -2, 1, 4, 7, 10, 13)**.

**Example 4**

How many **multiples of 5** there is between **101 and 999**?

*Resolution*

- The first
**multiple of****5**after**101**é**105**, therefore**= 105**; - The last
**multiple of 5**before**999**é**995**, therefore**= 995**; - The reason is
**5**because we are referring to**multiples of 5**.

Thus, we conclude that there are **179** **multiples of 5** in between **101** and **999**.

**Example 5**

Knowing that in a **PAN** the 2nd term is **9** and the 11th term is **45**, write this **PAN**:

*Resolution*

Let's write these terms as a function of** **and **r**:

We set up a system of equations:

Therefore, the **PAN** é **(5, 9, 13, 17,… )**.