Prove that the coefficient of $n$ is the common difference.

Question

Suppose the sequence <$a_n$> is an Arithmetic Progression if its $n^{th}$ term is a linear expression in $n$ then show that common difference is equal to the coefficient of $n$.

Answer 1

Let $$a_n=An+B$$then$$a_{n+1}=A(n+1)+B$$now$$a_{n+1}-a_n=An+A+B-An-B$$ $$=A$$ Hope it helps!!!