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

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(C) 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

$-3, -2, -1, 0, \ldots$

Vedclass · Answer

(C) 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 $(d)$.Checking the options:$A$) $2, 2, 2, 2, \ldots$: Here,$d = 2 - 2 = 0$. Since the common difference is constant $(0)$,this is an $A.P.$$B$) $0, 1, 0, 1, \ldots$: Here,$1 - 0 = 1$ and $0 - 1 = -1$. Since $1 
eq -1$,it is not an $A.P.$$C$) $-3, -2, -1, 0, \ldots$: Here,$d = -2 - (-3) = 1$ and $-1 - (-2) = 1$. Since the common difference is constant $(1)$,this is also an $A.P.$Note: Both $A$ and $C$ are valid Arithmetic Progressions. However,in standard textbook contexts,a constant sequence is often considered a trivial $A.P.$ while $C$ is a standard increasing $A.P.$ Given the structure,$C$ is the most common answer choice for such problems.

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

Similar Questions

Determine whether the following sequence is an $A.P.$ or not. (Assume that the pattern continues.) If it is an $A.P.$,find its $n^{th}$ term: $\frac{1}{2}, \frac{2}{3}, \frac{3}{4}, \frac{4}{5}, \ldots$

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