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?

Answer 1

(A) -3, 6, -9, -12, …
(B) -3, 20, -95, 480, …
(C) -3, 6, -9, 12, …
(D) -3, -20, -95, -480, …

Answer 2

I know that the answers cannot be B and D

Answer 3

you can toss out B and D

Answer 4

Yup that's what I said

Answer 5

\[f(2)=-2f(1)-f(0)\\
f(2)=-2\times 6-(-3)\\
f(2)=-12+3=-9\]

Answer 6

but both A and C have \(-9\) as the third number, so you need to compute \(f(3)\)

Answer 7

i.e. you need to compute
\[f(3)=-2\times f(2)-f(1)\]

Answer 8

f(3) = -2 * -9 - 6

Answer 9

f(3) = 12

Answer 10

So the answer is C

Answer 11

Right, answer is C?

Answer 12

yeah it is always C

Answer 13

Thank you so much!!