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**Hint:**Solution:

We will find the first two terms of the given AP using the given formula for the general term. Then we will Subtract $1^{\text{st}}$ term from the $2^{\text{nd}}$ term and hence find the common difference.

**Complete step by step solution:**

The common difference of an AP is the difference between any two consecutive terms of the AP. It is denoted by $d$

Now the first term of the AP is given by

$

{a_1} = 2(1) + 1 \\

\Rightarrow {a_1} = 3 \\

$

Now, the second term of the given AP

$

{a_2} = 2(2) + 1 \\

\Rightarrow {a_2} = 5 \\

$

So, the common difference is $d = {a_2} - {a_1} \Rightarrow d = 5 - 3 \Rightarrow d = 2$

**The common difference of the given AP is 2.**

**Note:**

It is important to know that the common difference is equal throughout the AP. So, instead of using the first two terms we could have used any two terms say $4^{th}$ and the $5^{th}$ term of the AP to calculate the common difference.

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