# Help please!!!! The table below shows the values of f(n) for different values of n: n 1 2 3 4 5 6 f(n) 1 2 2 4 8 32 Which recursive function best represents the values shown in the table?

2
by lalipapa123

2015-04-25T07:31:39+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

for , the th term can be obtained by multiplying previous two terms:

2015-04-25T07:51:36+05:30

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
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

click on thanks (blue button) above pls