Question

The following function defines a recursive sequence.

f(0)=-4
f(1)=12
f(n)=-3xf(n-1)-2xf(n-2); for n > 1

Which of the following sequences is defined by this recursive function?

-4, 12, -28, 60, ...
-4, -12, -28, -60, ...
-4, 12, -18, 54, ...
-4, 12, -18, -54, ...

Answer 1

@terenzreignz

Answer 2

Please help! D:

Answer 3

@cwrw238 Can you help me?

Answer 4

The notation is a little odd but the problem actually isn't that bad.

Answer 5

n represents the term of the function that you want to find.

Answer 6

Okay.

Answer 7

So, for n = 2, that means it's saying
\[f(2) = -3(f(1)) - 2(f(0))\]

Answer 8

We know both of those values (they're given) so we can just plug in.
\[f(2) = -3(12) - 2(-4)\]\[f(2) = -28\]

Answer 9

Now we know f(2), which means we can evaluate f(3), because f(3) is just
\[f(3) = -3(f(2)) - 2(f(1))\]

Answer 10

Do you follow?

Answer 11

Yes.

Answer 12

Ok. :D

Answer 13

:D Can you walk me through the evaluation real quick though? ._.

Answer 14

\[f(3) = -3(f(2) - 2(f(1))\]\[f(3) = -3(-28) - 2(12)\]
Simplify that. :)

Answer 15

Ah, thank you so much!

Answer 16

Okay, so I got 84 - 24 or, 60. What do I do with that?

Answer 17

That's the next entry in the sequence.

Answer 18

So far the sequence we've generated is -4, 12, -28, 60.

Answer 19

Is that all I need for the answer?

Answer 20

You tell me. :P

Answer 21

I think so.