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**Hint:**In this question, first of all, we will put the values of \[n = 1,2,3,4,...\] in the general term \[{a_n} = 2n + 1\] in order to get the Arithmetic progression after that take the difference between the terms of AP and the difference will be called as the common difference of the AP.

**Complete step by step solution:**We have been given general term of Arithmetic progression as \[{a_n} = 2n + 1\]

Now, we will put the values of \[n = 1,2,3,4,...\] in \[{a_n} = 2n + 1\] in order to get the AP.

For \[n = 1\] we get,

\[{a_1} = 2\left( 1 \right) + 1\]

\[ \Rightarrow {a_1} = 2 + 1\]

\[ \Rightarrow {a_1} = 3\]

For \[n = 2\] we get,

\[{a_2} = 2\left( 2 \right) + 1\]

\[ \Rightarrow {a_2} = 4 + 1\]

\[ \Rightarrow {a_2} = 5\]

For \[n = 3\] we get,

\[{a_3} = 2\left( 3 \right) + 1\]

\[ \Rightarrow {a_3} = 6 + 1\]

\[ \Rightarrow {a_3} = 7\]

For \[n = 4\] we get,

\[{a_4} = 2\left( 4 \right) + 1\]

\[ \Rightarrow {a_4} = 8 + 1\]

\[ \Rightarrow {a_4} = 9\]

Therefore, A.P. is \[3,5,7,9,...\]

Difference between 3 and 5 is 2.

Similarly,

Difference between 5 and 7 is 2 and

Difference between 7 and 9 is 2.

**Hence, Common difference of arithmetic progression is 2.**

**Note:**An arithmetic progression is a sequence of numbers such that the difference of any two successive members is a constant.

In an arithmetic progression the first term of a sequence is denoted by \[{a_1}\] and the difference of successive member is d which is also called as common difference since it’s common for all the successive numbers, then the nth term of sequence \[\left( {{a_n}} \right)\] is given by, \[{a_n} = {a_1} + \left( {n - 1} \right)d\].

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