Question

Which of the following sequence is an arithmetic sequence

• A. f(n) = an + b; n ∈ N
• B. f(n) = $k{r}^n,$ n ∈ N
• C. f(n) = (an + b) $k{r}^n,$, n ∈ N
• D. f(n) = $\frac{1}{a(n+\frac{b}{n})};$ n ∈ N

Answer 1

The correct option is A f(n) = an + b; n ∈ N

Sequence f(n) = an + b; n ∈ 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, ұ n ∈ N.