## Loser66 one year ago http://openstudy.com/study#/updates/55785893e4b0826b0eaff455

1. Loser66

My question on it is: No matter what the method I use, the answers must be the same, right? method 1) directly substitute f(n-1), f(n-2) to find f(n), we get d is the final answer.

2. Loser66

for the first question.

3. geerky42

Well, clearly if answer is not same, then you are incorrectly using method. :P

4. Loser66

How about this: f(n) = -4f(n-1) -3f(n-2) We can go backward like f(n+2) = -4 f(n+1) -3f(n)

5. Loser66

that give us the characteristic equation for recursive formula is: r^2 +4r+3 =0, $$r_1= -3$$ $$r_2= -1$$ Hence the general solution for it is $$f(n) = C_1 (-3)^n +C_2(-1)^n$$

6. Loser66

f(0) = -5, hence -5 = C1 + C2 f(1) = 20 , hece 20 = -3C1-C2 solve them, it gives me C1 = -15/2 C2 = 5/2

7. Nnesha

yes d is correct .... .-. $\rm f(2) = -4•f(2 -1) - 3•f(2 - 2)$$\rm f(2) = -4•f(1) - 3•f(0)$ =-65 :-)???

8. geerky42

@Nnesha Loser66 is more of looking for a way to find explicit formula.

9. Nnesha

otay.

10. Loser66

oh, I know my mistake. hihihi. it works well just the way I count f(3) is f(2) in the sequence. hehehe.. Thanks you all.

11. Loser66

@Nnesha my goal is to apply my knowledge in Discrete Math to put it in logic

12. Nnesha
13. Loser66

$$f(n) = \dfrac{5}{2}(-1)^n-\dfrac{15}{2} (-3)^n$$ f(2) , that is n = 2 , $$f(2) = \dfrac{5}{2} -\dfrac{15}{2}*9= 65$$ f(3) , that is n =3 , $$f(3) = \dfrac{5}{2}(-1)^3 -\dfrac{15}{2}(-3)^3=200$$

14. Loser66

oh, f(2) = -65 :)

15. Loser66

the first term is f(0) , next is f(1),

16. Loser66

That was my mistake. hehehe...

17. Nnesha

gO_OD job! @Loser66 ;-)

18. Loser66

haaaaaaaaaaaaaahahaha... thank you for the tough flower. @Nnesha

19. Nnesha

flower or chocolates ? Yw