Question

If nth term of an AP is an an+b then its common difference is

Answer 1

Answer: The answer is 'a'.

Step-by-step explanation:  We are to find the common difference of an A.P. if its n-th term is given by (an + b).

The n-th term of the A.P. is

$a_n=an+b.$

Therefore, the (n+1)-th term of the A.P. will be

$a_{n+1}=a(n+1)+b.$

We know that the common difference of an A.P. means the difference between two consecutive terms, so

$\textup{common difference},~d=a_{n+1}-a_n=(an+a+b)-(an+b)=a.$

Thus, the required common difference is 'a'.

Answer 2

Answer:

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