http://prntscr.com/b2d5wc
When it asks to show that x_n satisfies the difference equation, can you just sub x_n into the difference equation and prove that it equals to 0?
x_n = (31/19 * x_(n-1)) - (12/19 * x_(n-2))
SO if you sub it into 19x_n - 31x_(n-1) + 12x_(n-1) = 0
it just shows 0=0.
Or do you have to prove it in a different way?

Question

http://prntscr.com/b2d5wc
When it asks to show that x_n satisfies the difference equation, can you just sub x_n into the difference equation and prove that it equals to 0?
x_n = (31/19 * x_(n-1)) - (12/19 * x_(n-2))
SO if you sub it into 19x_n - 31x_(n-1) + 12x_(n-1) = 0 
it just shows 0=0.
Or do you have to prove it in a different way?

phi · Answer

yes, that is what they mean.  when you sub in for x_n, the equation is true (as shown by 0=0, which is true)

butterflydreamer · Answer

Cool, just checking because it seemed too simple haha.

butterflydreamer · Answer

With the n>=3 part, how would you show that is true?

Like since to find x_n (the length of each hop), you need the length of the prev hop [x_n(-1)] and the length of the hop before the prev hop [x_{n-2)], so n must be equal/greater than 3. 
I understand why n must equal to 3 or greater but i'm just not sure how to write it out.

phi · Answer

you don't have to show anything else.  the n>=3 is there so that x_(n-2) is defined
in other words, the equation does not apply for n less than 3

butterflydreamer · Answer

oh. :) okay! Thank you again!