Try taking the ratio of successive terms and difference of successive terms when to find a recursive relation for a function. Or, try taking the difference of n th term and n-2 nd term or their ratio. Check a few combinations.

Then see the values of the sequence obtained, if that matches with f(n), f(n-1), f(n-2) or their multiples. Some sequence will match.

n = 1 2 3 4 5 6

f(n) = 1 2 2 4 8 32

f(n-1) = - 1 * *__ 2 2 4 8 __ 32

f(n-2) = - - ** **__ 1 2 2 4 __ 8 32

2 f (n-1) = - 2 4 4 8 16

f(n)-f(n-1) = - 1 0 2 4 24

f(n)-2 f(n-1) = - 0 -2 0 0 16

f(n) - f(n-2) = - - 1 2 6 28

f(n) / f(n-1) = - 2 *1 2 2 4*

f(n) / f(n-2) = - - **2 2 4 8 **

f(n) / f(n-3) = - - - 4 4 16

It seems to be that only the data items highlighted are matching.

Now infer the relationship. f(n) / f(n-1) = f(n-2

* * f(n) = f(n-1) * f(n-2) , for 3 <= n <= 6

*OR, f(n+2) = f(n+1) * f(n) , for 1 <= n <= 4*

If we want the relation to be defined for the first two data items also, then we may define

f(-1) = 1/2 and f(0) = 2, in that case,

f (n) = f (n - 1) f (n - 2), for 1 <= n <= 6