Find the common difference of the A.P. and write the next two terms :$0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, ………..$

Given:

Given A.P. is $0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, ………..$

To do:

We have to find the common difference and write the next two terms of the given A.P.

Solution: 

 The common difference of an A.P. is the difference between any two consecutive terms.

Here,

$a_1=0, a_2=\frac{1}{4}, a_3=\frac{1}{2}, a_4=\frac{3}{4}$

$d=a_2-a_1=\frac{1}{4}-0=\frac{1}{4}$

$a_5=a_4+d=\frac{3}{4}+\frac{1}{4}=\frac{3+1}{4}=\frac{4}{4}=1$

$a_6=a_5+d=1+\frac{1}{4}=\frac{1\times4+1}{4}=\frac{5}{4}$

The common difference of the given A.P. is $\frac{1}{4}$ and the next two terms are $1$ and $\frac{5}{4}$.