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 5 12 29 70


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

Answer 1

@ganeshie8 plz help

Answer 2

do you know how to do a sequence? @hero a lil help

Answer 3

well i know that we replace the number oh wait...
Arithmetic Recursive Formula
Examine the recursive formula given the arithmetic sequence 2, 5, 8, 11, …

The first term of the sequence is 2, and the common difference is 3.
f(1) = 2, d = 3

To find the next term in the sequence, the common difference is added to the previous term.
f(2) = f(1) + d = 2 + 3 = 5
f(3) = f(2) + d = 5 + 3 = 8

To find the nth term of this sequence, the common difference would be added to the term before it. This is the generic form for an arithmetic recursive formula.
f(n) = f(n – 1) + d
The variable d is the common difference and n > 0.

Check to see that this works by finding the fourth term of the sequence. (n = 4)

Answer 4

is it a @muzzack ?

Answer 5

@ganeshie8 plz help

Answer 6

well what do you think??

Answer 7

no idea lol

Answer 8

well believe ur gut

Answer 9

which rule fits?

Answer 10

idk lol

Answer 11

so the question becomes .. why dont you know? you have 4 options to test out, and they give you the values ....

Answer 12

what are the values? what are you supposed to do with the options? (you can see im not really good at this stuff)

Answer 13

the values are listed for you already ... for exmaple, when n=3, f(3)=5

you have to determine which rule best defines the function.

Answer 14

notice that there is no n=0 .. so f(n-3) means nothing to us when n=3. what does this tell us about options with f(n-3) in them?

Answer 15

tht f(0)=0 i think?

Answer 16

f(0) is not defined.

Answer 17

i meant tht lol

Answer 18

so i have to do f(?)

Answer 19

so, we can rule out any option that has f(n-3) in it since they all say n starts at 3, and f(3-3) is simply undefined.

Answer 20

So there is only a and c left over

Answer 21

right, so now lets follow the rules defined:

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

f(3) = 2f(3 -1) f(3 - 2)
f(3) = 2f(2) f(1) , is this true?

---------------------------------
f(n) = 2f(n -1) + f(n - 2)
f(3) = 2f(3 -1) + f(3 - 2)
f(3) = 2f(2) + f(1), or is this true?

Answer 22

hold on i have to substitute the values in the n right? give me a few mins to do tht

Answer 23

yes

Answer 24

The second one right @amistre64 ?

Answer 25

yes: 5 = 2(2)+1 is true.

Answer 26

Thank You!

Answer 27

now lets see if it works for the next value, im sure it does,

12 = 5(2) + 2 ... seems to work fine