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
$$\begin{gathered} a_1=2(1)+1 \\ \Rightarrow a_1=3 \end{gathered}$$
Now, the second term of the given AP
$$\begin{gathered} a_2=2(2)+1 \\ \Rightarrow a_2=5 \end{gathered}$$
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.