Question

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

Answer 1

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.