Question

Which of the following sequence is an arithmetic sequence.

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

Answer 1

Answer: (A)

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

Answer 2

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

Putting we get the sequence

$( a + b ) , ( 2 a + b ) , ( 3 a + b ) , \ldots \ldots \ldots$ 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 $n ^ { t h }$ term of an A.P. is of the form $a n + b , \forall n \in N$ .