## anonymous one year ago 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, …

1. freckles

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

2. anonymous

okay, so what is the next step?

3. freckles

replacing n with 2

4. freckles

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

5. anonymous

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

6. anonymous

I'm not sure what the third term is.

7. freckles

it is f(2)

8. freckles

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

9. freckles

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

10. anonymous

oh okay.

11. anonymous

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?

12. freckles

$f(n) = -4•f(n -1) - 3•f(n - 2) \\ f(2)=-4 \cdot f(2-1)-3 \cdot f(2-2) \\ f(2)=-4 \cdot f(1)-3 \cdot f(0)$ 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

13. freckles

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

14. anonymous

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

15. freckles

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

16. anonymous

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

17. freckles

sure

18. freckles

one more I think

19. anonymous

Okay I'll tag you.