Question

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?

-3, 6, -9, -12, …
-3, 20, -95, 480, …
-3, 6, -9, 12, …
-3, -20, -95, -480, …

Answer 1

You know it's the first or third option from what you are given.

\[f(2)=-2 \times f(1) - f(0) = (-2)(6)-(-3)=-9.\].

Can you find the last term in the sequence?

Answer 2

-12?

Answer 3

For the first term, n=0. So you need f(0), which is given to you. The second term, n=1, so f(1) is needed. This was also given to you. Then we calculated the third term, f(2).

To calculate the last term, n=3, so you want to do \[f(3)=-2 \times f(2) - f(1)\] Is this -12?

Answer 4

Negative times a negative equals a positive right?

Answer 5

Yes. So the answer is?

Answer 6

-2 x f(2) = 12

Answer 7

oops soory

Answer 8

got mixed with something else lol

Answer 9

-2 x f(2) = 18 - f(1) = 12

Answer 10

Correct :)

Answer 11

can you help me with a couple other questions?

Answer 12

Sure. What else do you have?

Answer 13

For the function y = f(x), what is the ordered pair for the point on the graph when x = b - 2?

(b - 2, f(b -2))
(x, f(b))
(x, b - 2)
(b - 2, f(b))

I think its A

Answer 14

Actually C i think would be correct

Answer 15

Your first answer was correct. Can you justify why?

Answer 16

That's the part im kinda confused on. I know that if x is replaced with b-2 it'll look like this f(b-2) but why is the y also b-2? Isn't the x only b-2?

Answer 17

Each little point on the xy-plane is a coordinate of the form (x,y).

Now the question tells you y = f(x) for the particular graph of f(x). So each coordinate on this graph is defined by ( x , f(x) )

Answer 18

Oh ok

Answer 19

So what is the coordinate when x = b-2?

Answer 20

(b-2, f(b-2)

Answer 21

Yes. For x = b-2, the point on the graph is ( b-2, f(b-2) )

Answer 22

Thanks!

Answer 23

No problem!