Solve Complex Function: Step-by-Step Guide

[trojsi]

Hi,
please find attached the problem and the answer. I can't anderstand the first and second step of the answer. I only need a link for the topic or maybe method the used. Bdw I haven't tried to figure out the second answer but for now I only need help tackling the first one.

 

[Mark44]

There is no attachment...

 

[trojsi]

thanks for telling.. I uploaded it now :)

 

[HallsofIvy]

I have the feeling I have done this before!

You have the equation $f(n)= 15^n+ 8^{n-2}$ and want to write f(n+1)- 8 f(n) as a multiple of $15^n$.

Okay, $f(n+1)= 15^{n+1}+ 8^{n+1- 2}$$= 15^{n+1}- 8^{n-1}$ and $8f(n)= 8(15^n)- 8^{n-2})=$$8(15^n)- 8(8^{n-2})=$$8(15^n)- 8^{n-1}$

Now, when you subtract the two "$8^{n-1}$" terms cancel and you get $15^{n+1}- 8(15^n)= 15(15^n)- 8(15^n)= (15- 8)15^{n+1}$.