Question

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 4 16 128 4096


Which recursive function best represents the values shown in the table?
f(1) = 1, f(2) = 2, f(n) = f(n -3) + f(n - 2); n > 2

f(1) = 1, f(2) = 2, f(n) = f(n -3) f(n - 2); n > 2

f(1) = 1, f(2) = 2, f(n) = 2f(n -1) + f(n - 2); n > 2

f(1) = 1, f(2) = 2, f(n) = 2f(n -1) f(n - 2); n > 2

Answer 1

@amistre64

Answer 2

what do we know about a recursive function ... what does it tell us?

Answer 3

notice that all the options differ only by the function rule that they state. so the rest of it is eye clutter. which rule defines the sequence?

Answer 4

I'm not sure. :/

Answer 5

tell me whats confusing you about the function rules ...

Answer 6

I just dont know what to do to see if the values match up with the functions.

Answer 7

f(n) = f(n -3) + f(n - 2)

notice that there are 3 terms to deal with, and the rule for this one is just saying that the new terms is the sum of the 2 before it




f(n) = f(n -3) f(n - 2), and this one is saying its the product of the 2 terms before it




the rest are read in similar mathical nomenclatures

Answer 8

one minor thing to note is that there is no f(0), so having some f(n-3) for n=3 is simply undefined and cannot be worked out. so those first 2 options are errors just by default.

Answer 9

f(n) = 2f(n -1) + f(n - 2), let n=3

f(3) = 2f(3-1) + f(3 - 2)

f(3) = 2f(2) + f(1)

4 = 2(2) + 1 ... is not right either


so work the rule for the last option to verify

Answer 10

Do I plug in 3 for n like you did?

Answer 11

id hope so lol

Answer 12

for n>2 means that n=3,4,5,6,...

Answer 13

so testing it out for n=3 at lest lets us know its good for n=3

Answer 14

Thanks! :) The last one is definitely the correct answer.