Deranged numbers

Consider natural numbers 1,2,3,.......,n-1,n

Further consider n positions at which these are to be placed given that no number occupies its corresponding position.( eg. 1 does not come on first position, 2 does not come on second position etc.)

Let f(n) be the number of ways in which first n natural numbers numbers can be placed at n positions according to the above given condition.

Given that for some natural number n

$\frac{f(n-1)}{f(n+1)}$ = a

$\frac{f(n)}{f(n+1)}$ = b

Then-