# Iterative formulas

1. Mar 5, 2009

### DeanBH

1. The problem statement, all variables and given/known data

First of all this is revision not homework =)

question is Xn+1 = Cuberoot ( 17.5-2xn)

answer lies between 2 and 3. i know the answer is 2.34 but what i don't get is why it is
xn+1 = equation, because when you put xn=2.34 into the equation you get 2.34 out.
shouldnt get 3.34 out if its xn+1. whats the purpose of the n+1!!

2. Mar 5, 2009

### dirk_mec1

xn and xn+1 both go (in this convergent case) to a limit call it L. Now substitute L for xn and xn+1 and solve the equation.

3. Mar 5, 2009

### DeanBH

i don't think you understand what i'm confused with,

i know the answer is 2.34 so i put it in to check

xN+1 = cuberoot(17.5-2xn)

3.34=cuberoot(17.5-2*2.34)
3.34=2.34

do you understand what i dont understand.

4. Mar 5, 2009

5. Mar 5, 2009

### yyat

If you mean

$$x_{n+1}=(17.5+2x_n)^{1/3}$$

then the answer is $$\lim_{n\to\infty}x_n=2.34$$, and this solution can be found as dirk_mec1 described.

But if you mean

$$x_n+1=(17.5+2x_n)^{1/3}$$

then $$x_n=1.44$$ for all $$n$$.