Question

Is the following an A.P.? If it form an A.P. Find the common difference $d$ and write three more terms.

$2,\frac{5}{2},3,\frac{7}{2}\dots .$

Answer 1

Step 1. Find the common difference.

The given sequence is $2,\frac{5}{2},3,\frac{7}{2}\dots .$

The common difference is

$$\begin{gathered} \frac{5}{2}-2=\frac{1}{2} \\ 3-\frac{5}{2}=\frac{1}{2} \\ \frac{7}{2}-3=\frac{1}{2} \end{gathered}$$

Since, the common difference is same every time.

Therefore, $d=\frac{1}{2}$ and the given series are in A.P.

Step 2. Find the next three terms of an A.P.

The next three terms are:

$\begin{array}{rcl}\frac{7}{2}+\frac{1}{2}& =& 4\\ 4+\frac{1}{2}& =& \frac{9}{2}\\ \frac{9}{2}+\frac{1}{2}& =& 5\end{array}$

Yes, the given sequence is an A.P. and common difference is $d=\frac{1}{2}$ and the next three terms are $4,\frac{9}{2},5$.