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 where the difference between any two consecutive terms is constant. This constant is c

Vedclass · Accepted Answer

$5, 15, 25, 35, \ldots$

Vedclass · Answer

(C) An Arithmetic Progression $(A.P.)$ is a sequence of numbers where the difference between any two consecutive terms is constant. This constant is called the common difference $(d)$.Checking the options:Option $A$: $3, 3, 3, 3, \ldots$. Here,$d = 3 - 3 = 0$. Since the difference is constant,this is an $A.P.$Option $B$: $2, 22, 222, 2222, \ldots$. Here,$22 - 2 = 20$ and $222 - 22 = 200$. Since $20 
eq 200$,it is not an $A.P.$Option $C$: $5, 15, 25, 35, \ldots$. Here,$15 - 5 = 10$ and $25 - 15 = 10$. This is also an $A.P.$ with $d = 10$.Option $D$: $4, -4, 4, -4, \ldots$. Here,$-4 - 4 = -8$ and $4 - (-4) = 8$. Since $-8 
eq 8$,it is not an $A.P.$Note: Both $A$ and $C$ are technically arithmetic progressions. However,in standard textbook contexts,a sequence with a common difference of $0$ is a trivial $A.P.$ while $C$ is a standard $A.P.$ with a non-zero common difference. Given the structure,$C$ is the most representative answer.

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

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