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8. Sequences and Series
easy
Which of the following sequence is an arithmetic sequence
A
$f(n) = an + b;\,n \in N$
B
$f(n) = k{r^n};\,n \in N$
C
$f(n) = (an + b)\,k{r^n};\,n \in N$
D
$f(n) = \frac{1}{{a\left( {n + \frac{b}{n}} \right)}};\,n \in N$
Solution
(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,
$an + b,\;\forall n \in N$.
Standard 11
Mathematics
