# Math Help - linear recureence sequences

1. ## linear recureence sequences

(c) Consider the linear recurrence sequence
x
1 =23,xn+1 =1.3xn 12
(
n =1,2,3,...).
(i)
Find a closed form for the sequence.
[
4]
(ii) Use the closed form to find the eighth term of the sequence,
correct to four significant figures.
[
1]
(iii) Describe the long-term behaviour of the sequence.
[
2]

2. You should find that
$x_o=\frac{35}{1.3}$
$x_1=1.3 \cdot x_o - 12$
$x_2=1.3 \cdot (1.3 \cdot x_o - 12) -12 = 1.3^2 \cdot x_o - (1.3 + 1 ) \cdot 12$
$x_3=1.3^3 \cdot x_o - (1.3^2 + 1.3 + 1 ) \cdot 12$
$x_n=1.3^n \cdot x_o - (1.3^{n-1} + 1.3^{n-2} + ... + 1.3 +1 ) \cdot 12$
You alright for number two and I guess that by computing some value you can do number 3 alone.