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

1.	If nth term of an AP is an+b then its common difference
Answer» 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{tex}a_n=an+b.{/tex}Therefore, the (n+1)-th term of the A.P. will be{tex}a_{n+1}=a(n+1)+b.{/tex}We know that the common difference of an A.P. means the difference between two consecutive terms, so{tex} {common difference},~d=a_{n+1}-a_n=(an+a+b)-(an+b)=a.{/tex}Thus, the required common difference is \'a\'.

Discussion