If the average of $9$ consecutive even numbers is $132$, find the difference between the first and the last numbers.

Method 1: Direct Formula
For $n$ consecutive even or odd numbers, the difference between the first and the last number is always given by the formula:

$$\text{Difference}=2\times (n-1)$$

Here, $n=9$:

$$\text{Difference}=2\times (9-1)=2\times 8=16$$

Method 2: Step-by-step Representation
Let the $9$ consecutive even numbers be represented as:

$$x,x+2,x+4,x+6,x+8,x+10,x+12,x+14,x+16$$

Here, the first number is $x$ and the last number is $x+16$.

The difference between the first and the last number is:

$$\text{Difference}=(x+16)-x=16$$

(Note: The actual value of the average is not required to find this difference).