Prove $10^{n+1}+3\cdot 10^n+5$ is divisible by $9$? How do I prove that an integer of the form $10^{n+1}+3\cdot 10^{n}+5$ is divisible by $9$  for $n\geq 1$?I tried proving it by induction and could prove it for the Base case n=1. But  got stuck while proving the general case. Any help on this ? Thanks. 

$10^{n+1}+3\cdot 10^{n}+5=10^{n}(10+3)+5=1300\cdots05$ has digit sum equal to $9$ and so is a multiple of $9$.
