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

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Solution

Step 1. Find the common difference:
The AP is $6,12,18,...$
Here, $a_{1} = 6, a_{2} = 12, a_{3} = 18$ .
The common difference of AP is,
$\begin{array}{rcl} \Rightarrow & d = a_{2} - a_{1} \\ = & 12-6 \\ = & 6 \end{array}$
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 $24, 30$ .

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