Which of the following sequences is an A.P.? | vedclass

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(B) An Arithmetic Progression $(A.P.)$ is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant d

Vedclass · Accepted Answer

$1, \frac{1}{2}, 0, -\frac{1}{2}, \ldots$

Vedclass · Answer

(B) An Arithmetic Progression $(A.P.)$ is a sequence of numbers in which the difference between any two consecutive terms is constant. This constant difference is called the common difference $(d)$.Let us check the options:Option $A$: $\frac{1}{3} - \frac{1}{2} = -\frac{1}{6}$,while $\frac{1}{4} - \frac{1}{3} = -\frac{1}{12}$. Since $-\frac{1}{6} 
eq -\frac{1}{12}$,it is not an $A.P.$Option $B$: $\frac{1}{2} - 1 = -\frac{1}{2}$,$0 - \frac{1}{2} = -\frac{1}{2}$,and $-\frac{1}{2} - 0 = -\frac{1}{2}$. Since the common difference $d = -\frac{1}{2}$ is constant,this is an $A.P.$Option $C$: $6 - (-3) = 9$,while $-6 - 6 = -12$. Since $9 
eq -12$,it is not an $A.P.$Option $D$: $\frac{1}{5} - 5 = -\frac{24}{5}$,while $3 - \frac{1}{5} = \frac{14}{5}$. Since $-\frac{24}{5} 
eq \frac{14}{5}$,it is not an $A.P.$Therefore,the correct option is $B$.

Which of the following sequences is an $A.P.$?

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