It does not exist

$\large \dbinom{n}{a} \ , \ \dbinom{n}{a+1} \, \ \ldots \ , \ \dbinom{n}{a+b}$

For positive integers $n,a,b$ with $n > a+b$ , the above sequence of numbers follow an arithmetic progression. Find the maximum value of $b$ .

Clarification : The numbers above are all written in binomial coefficient form.