Question

Examine that the sequence $\mathrm{7,13,19,25,...}$ is an AP. Also, find the common difference.

Answer 1

Step 1. To check the sequence $\mathrm{7,13,19,25,...}$ is AP or not:

Here, $a_1=7,a_2=13,a_3=19$.

$\begin{array}{rcl}& \Rightarrow & a_2-a_1=13-7\\ & =& 6\\ & \Rightarrow & a_3-a_2=19-13\\ & =& 6\\ & \Rightarrow & a_2-a_1=a_3-a_2\end{array}$

Therefore, the sequence $\mathrm{7,13,19,25,...}$ forms an AP.

Step 2. Find the common difference:

The common difference between the first and second term is,

$\begin{array}{rcl}& \Rightarrow & {\text{a}}_2-{\text{a}}_1=13-7\\ & =& 6\end{array}$

Therefore, it is in AP with a common difference $6$.