Question

Find the common difference and the next two terms of the AP: $6,12,18,...$

Answer 1

Step 1. Find the common difference:

The AP is $\mathrm{6,12,18,...}$

Here, $a_1=6,a_2=12,a_3=18$.

The common difference of AP is,

$\begin{array}{rcl}& \Rightarrow & d=a_2-a_1\\ & =& \mathrm{12-6}\\ & =& 6\end{array}$

Hence, the common difference $d=6$.

Step 2. Calculate the next two terms of the AP $6,12,18,...$:

$\begin{array}{rcl}& \Rightarrow & a_4=a_3+d\\ & =& 18+6\\ & =& 24\end{array}$

$\begin{array}{rcl}& \Rightarrow & a_5=a_4+d\\ & =& 24+6\\ & =& 30\end{array}$

Therefore, the required common difference is $6$ and the next two terms are $24,30$.