Question

Question 2 (i)
Verify that each of the following is an AP and then write its next three terms.
$0,\frac{1}{4},\frac{1}{2},\frac{3}{4},\cdots$

Answer 1

$Here,a_1=0,a_2=\frac{1}{4},a_3=\frac{1}{2}and{a}_4=\frac{3}{4}$
$a_2-a_1=\frac{1}{4},a_3-a_2=\frac{1}{2}-\frac{1}{4}=\frac{1}{4},a_4-a_3=\frac{3}{4}-\frac{1}{2}=\frac{1}{4}$
$\therefore a_2-a_1=a_3-a_2=a_4-a_3$
Since the difference between successive terms are same, it forms an AP. The next three terms are,
$a_5=a_1+4d$
$=a+4\left(\frac{1}{4}\right)=1,a_6=a_1+5d=a+5\left(\frac{1}{4}\right)=\frac{5}{4}$
$a_7=a+6d=0+\frac{6}{4}=\frac{3}{2}$