Question

Question 1 (v)
Which of the following form an AP? Justify your answer.
$\frac{1}{2},\frac{1}{3},\frac{1}{4},\cdots$

Answer 1

$Here,t_1=\frac{1}{2},t_2=\frac{1}{3}and{t}_3=\frac{1}{4}$
$t_2-t_1=\frac{1}{3}-\frac{1}{2}=\frac{2-3}{6}=-\frac{1}{6}$
$t_3-t_2=\frac{1}{4}-\frac{1}{3}=\frac{3-4}{12}=-\frac{1}{12}$
Clearly, the difference between the successive terms is not the same.
Therefore, the given numbers do not form an AP.