Which of the following sequences is an arithm | vedclass

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(A) The sequence $f(n) = an + b;\;n \in N$ is an $A.P.$ (Arithmetic Progression).By substituting $n = 1, 2, 3, 4, \dots$,we obtain the sequence:$(a +

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$f(n) = an + b;\,n \in N$

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(A) The sequence $f(n) = an + b;\;n \in N$ is an $A.P.$ (Arithmetic Progression).By substituting $n = 1, 2, 3, 4, \dots$,we obtain the sequence:$(a + b), (2a + b), (3a + b), \dots$Here,the first term $A = (a + b)$ and the common difference $d = (2a + b) - (a + b) = a$.Since the common difference is constant,the sequence is an $A.P.$Alternatively,the $n^{th}$ term of an $A.P.$ is always a linear expression in $n$ of the form $an + b$ for all $n \in N$.

Which of the following sequences is an arithmetic sequence?

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