Question

The following function defines a recursive sequence:

f(0) = -5

f(1) = 20

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

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

-5, -20, -65, -200, …

-5, 20, -92, 372, …

-5, -24, -92, -372, …

-5, 20, -65, 200, …

Answer 1

you are given the first two terms in the sequence -5,20,...
so you can definitely eliminate one of those choices anyways
to find the third replace n with 2

Answer 2

okay, so what is the next step?

Answer 3

replacing n with 2

Answer 4

then using that f(0)=-5 and f(1)=20
to find f(2) (which is the third term)

Answer 5

I eliminated A and C. So I am left with B or D.

Answer 6

I'm not sure what the third term is.

Answer 7

it is f(2)

Answer 8

since f(0) is first term
and f(1) is second
so f(2) is the third

Answer 9

that is why I'm asking you to replace n with 2

Answer 10

oh okay.

Answer 11

Don't if I plug in the -5 and the 20 into the term won't I get -65? That is what I got at first but I'm not sure if that is right?

Answer 12

\[f(n) = -4•f(n -1) - 3•f(n - 2) \\ f(2)=-4 \cdot f(2-1)-3 \cdot f(2-2) \\ f(2)=-4 \cdot f(1)-3 \cdot f(0)\]
remember f(1) is 20 and f(0) is -5
so you have
\[f(2)=-4 \cdot 20-3 \cdot (-5)\]
and yes -80+15=-65

Answer 13

so your work is done now
you can move on to next problem
good job

Answer 14

oh okay, so that would mean if I continued with the process I would ghet 200 next right?

Answer 15

if you don't get 200 then none of the choices are correct :p

Answer 16

I did get 200, so it is D. Thanks so much! Can you help me with a few more?

Answer 17

sure

Answer 18

one more I think

Answer 19

Okay I'll tag you.