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The common difference of an AP whose general term is given by ${a_n} = 2n + 1$ is

Last updated date: 18th Jun 2024
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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.

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.