Which of the following sequence is an arithmetic sequence - Vidyadip

MCQ

Which of the following sequence is an arithmetic sequence

✓
$f(n) = an + b;\,n \in N$
B
$f(n) = k{r^n};\,n \in N$
C
$f(n) = (an + b)\,k{r^n};\,n \in N$
D
$f(n) = \frac{1}{{a\left( {n + \frac{b}{n}} \right)}};\,n \in N$

✓

Answer

Correct option: A.

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

a
(a) Sequence $f(n) = an + b;\;n \in N$ is an $A.P.$

Putting $n = 1,\;2,\;3,\;4,\;..........,$ we get the sequence

$(a + b),\;(2a + b),\;(3a + b),.........$ which is an $A.P.$

Where first term $(A) = (a + b)$ and common difference $d = a$.

Aliter : As we have mentioned in theory part that ${n^{th}}$ term of an $A.P.$ is of the form,

$an + b,\;\forall n \in N$.

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