Question

Find the common difference and the next two terms of the AP: $\frac{1}{3},\frac{4}{3},\frac{7}{3},\dots$

Answer 1

Step 1. Find the common difference:

The AP is $\frac{1}{3},\frac{4}{3},\frac{7}{3},\dots$

Here, $a_1=\frac{1}{3},a_2=\frac{4}{3},a_3=\frac{7}{3}$.

The common difference of AP is,

$\begin{array}{rcl}& \Rightarrow & d=a_2-a_1\\ & =& \frac{4}{3}-\frac{1}{3}\\ & =& 1\end{array}$

Hence, the common difference $d=1$.

Step 2. Calculate the next two terms of the AP $\frac{1}{3},\frac{4}{3},\frac{7}{3},\dots$:

$\begin{array}{rcl}& \Rightarrow & a_4=a_3+d\\ & =& \frac{7}{3}+1\\ & =& \frac{10}{3}\end{array}$

$\begin{array}{rcl}& \Rightarrow & a_5=a_4+d\\ & =& \frac{10}{3}+1\\ & =& \frac{13}{3}\end{array}$

Therefore, the required common difference is $1$ and the next two terms are $\frac{10}{3},\frac{13}{3}$.