Question

The following function defines a recursive sequence:
f(0) = -2

f(1) = 8

f(n) = -4•f(n -1) - 3•f(n - 2); for n > 1

Which of the following sequences is defined by this recursive function? (4 points)


-2, 8, -26, -80, …
-2, 8, -26, 80, …
-2, 12, -44, 180, …
-2, -12, -44, -180, …

Answer 1

Plug in f(2) so where ever there is a n plug in a 2 there as following \[f(2) = -4 \times f(2-1) - 3 \times f(2-2) \implies f(2) = -4 f(1)-3 f(0)\] and then you can figure out the rest as we now have are given the other terms.

Answer 2

What do I do now?

Answer 3

Notice how we have f(1) and f(0) there now we can simply plug in the given values for f(1) and f(0)

Answer 4

\[f(2) = -4(8)-3(-2)\] what does that equal?

Answer 5

f(2) -36 + 6

Answer 6

?

Answer 7

No try again

Answer 8

What am I supposed to do ??

Answer 9

I explained it, read it over. What is -4 times 8?

Answer 10

-32

Answer 11

what is -32+6?

Answer 12

-26

Answer 13

Correct, so now we have our first three terms, -2,8,-26 now do the same thing to find the fourth term

Answer 14

put them together?

Answer 15

No, you're looking for a sequence, so like a pattern, 1,2,3,4...so we have f(0),f(1),f(2), now we need f(3)

Answer 16

I don't know how to do that!

Answer 17

Do the same steps as I showed you but for f(3) but now we have f(2) = -26

Answer 18

What?

Answer 19

You need to find the first four terms, I showed you how to get your third term now you have to find the fourth term, just read through what I said above. The first comment.

Answer 20

I have no idea what this means but thanks anyways..

Answer 21

Scroll up and just try to understand dude

Answer 22

I did try but I don't get it.

Answer 23

We're given a pattern for f(n) all we have to plug in is the values we're looking for, we have the first three, now we need the fourth, so \[f(3) = -4 \times f(3-1)-3 \times f(3-2)\]

Answer 24

What do I do??