Linear Recurrence Relations

Question

I'm having trouble understanding the process of solving simple linear recurrence relation problems. The problem in the book is this: $$ 0=a_{n+1}-1.5a_n,\ n \ge 0 $$ What is the general process, and purpose, of solving this? Unfortunately there is a very large language barrier between my professor and myself, which is quite a problem.

Answer 1

The general solution to the equation

$$a_{n+1} = k a_n$$

is

$$a_n = B \cdot k^n$$

for some constant $B$, which is related to an initial condition.

Answer 2

For this one, you can rewrite it as $a_{n+1}=1.5a_n$ and then continue substituting to get $a_{n+1}=1.5a_n=(1.5)^2a_{n-1}$ and see $a_n=1.5^na_0$

Answer 3

$a(n)=1,5^{n}a(0)$ when $a(0)$ should be given.