A6 A sequence $a_{n}, n \in \mathbb{N}$ is given, for which $a_{n+1}-a_{n}=5$ and $a_{1}=37$. Which of the following numbers is a term of this sequence?
(A) 500
(B) 1000
(C) 1500
(D) 2000
(E) none of the above
A6. We find that this is an arithmetic sequence with the first term 37 and a common difference of 5. The general term is $a_{n}=37+(n-1) \cdot 5=32+5n=5(6+n)+2$. None of the given numbers have a remainder of 2 when divided by 5, so the correct answer is E.

## Set B