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OZO: Urgent

Let r satisfy the equation r^2 = r + 1.
Show that the sequence s_n = ar^n, where A is constant, satisfies the fibonacci equation f_n = f_(n-1) + f_(n-2).

I'm not sure how to show this.

I know that f_1 = 1 & f_2 = 2

f_1 = 1
f_2 = 2
f_3 = f_2 + f_1
f_4 = f_3 + f_2

So

s_3 = s_2 + s_1 = Ar + Ar
s_4 = s_3 + s_2 = Ar + Ar + Ar
s_5 = s_4 + s_3 = Ar + Ar + Ar + Ar + Ar
s_6 = s_5 + s_4 = Ar + Ar + Ar + Ar + Ar + Ar + Ar + Ar

I'm not sure what i'm doing ;/

-Brian

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sunnycoder

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SOLUTION

ozo

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BrianGEFF719

ASKER

Hey Sunnycoder,

About 2 1/2yrs ago you used to help me with algebra...I've since advanced to higher levels of math, but good to see you again :)

Brian

BrianGEFF719

ASKER

Ozo, if you've got a few minutes i've got an easy physics one for you...

BrianGEFF719

ASKER

https://www.experts-exchange.com/questions/21818690/Ball-in-freefall.html

BrianGEFF719

ASKER

I dont quite understand this step:

ar^(k-1) + ar^(k-2) = ar^(k-2)) * (1+r)

How do you guys get this?

sunnycoder

ar^(k-2) is common in both terms

BrianGEFF719

ASKER

Sunnycoder, thanks a lot!

sunnycoder