Question

HELP!!!!!!!

The following function defines a recursive sequence:

f(0) = -3

f(1) = 6

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

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


Answer Choices:

-3, 6, -9, -12, …

-3, 20, -95, 480, …

-3, 6, -9, 12, …

-3, -20, -95, -480, …

Answer 1

recursive sequences bounce off the last term in a sequence, so basically we start off with a given one, and we're told ( makes 2 and two makes three....)

Answer 2

I'm lost

Answer 3

Ok, I'll start with something simple, a sequence, which is just a list of numbers that is recursive might look like this one

1,1,2,3,5,8,13,21,34......

I'm pretty sure you've seen this before (it's called the Fibonnacci sequence and is defied recursively as fn = fn-1 + fn-2 where n>3 or n=3)
Baiscally that means you add 1 to 1 to make 2 1 to 2 to make 3 2 to 3 to make 5 3 to 5 to make 8 5 to 8 to make 13 and so on

Answer 4

Ok so how would I apply this sequence into the question I asked? @doulikepiecauseidont

Answer 5

Well they give you the first two terms of the sequence which needs to be given for a recursive sequence how one works is that they give the first 2 or three then say you do something to the previous number to get a new number, of course you couldn't do anything if hey didn't give you a number to start of with

Answer 6

And for started all we have to look at is A and C since they gave us the first two terms and B and D don't have those two terms (-3, and 6)

So looking at our f(n) equation, since there's 4 numbers in our sequence we need f(2) and f(3) since we alread have
f(0)=-3
&
f(1)=6

f(0)+f(1)+f(2)+f(3)=4 terms, follow so far?

Answer 7

Yes

Answer 8

OK and f(n)=-2•f(n -1) - f(n - 2)

All we have to do to find f(2) and f(3) is to replace all our n's with 2 and get our 3rd number and then replace all the 2's with 3's to get our 4th number I'll fill int he equation and you tell me what you get, now rememeber this is recursive so you have to find f(2) before you find f(3) since f(2) will be part of the equation for f(3), you'll see

f(2)= -2f(2-1)-f(2-1)
= -2f(1)-f(1)

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

Now when we solve we'll get our 3rd and 4th number and that'll be our answer

Answer 9

Okay I got it thanks

Answer 10

Yw