Question

Find the common difference of the A.P.: $0,\frac{1}{4},\frac{1}{2},\frac{3}{4},...$

Answer 1

Given A.P is,

$0,\frac{1}{4},\frac{1}{2},\frac{3}{4}\dots$

$\Rightarrow$first term of this A.P is $a_1=0$

$\Rightarrow$second term of this A.P is $a_2=\frac{1}{4}$

$\Rightarrow$third term of this A.P is $a_3=\frac{1}{2}$

$\Rightarrow$fourth term of this A.P is $a_4=\frac{3}{4}$

common difference of an A.P is given by $d=a_{n+1}-a_n$

putting $n=1$ in above equation

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

lly, if $n=2$

then $d=a_3-a_2=\frac{1}{2}-\frac{1}{4}=\frac{1}{4}$

hence, common difference $d=\frac{1}{4}$