Question

Using xn+1 = 1 -(3/x^2)
with x0 = -2.5
Find the values of X1, X2 and X3 using iteration​

Answer 1

Answer:

The values of $x_{1}$, $x_{2}$ and $x_{3}$ are 0.52, -10.094 and 0.971.

Step-by-step explanation:

Let $x_{n+1} = 1-\frac{3}{x_{n}^{2}}$ be the recurrence formula and $x_{o} = -2.5$. The first values of this recurrence are, respectively:

$x_{1}$:

$x_{1} = 1 - \frac{3}{x_{o}^{2}}$

$x_{1} = 1-\frac{3}{(-2.5)^{2}}$

$x_{1} = 0.52$

$x_{2}$:

$x_{2} = 1-\frac{3}{x_{1}^{2}}$

$x_{2} = 1-\frac{3}{0.52^{2}}$

$x_{2} = -10.094$

$x_{3}$:

$x_{3} = 1-\frac{3}{x_{2}^{2}}$

$x_{3} = 1 - \frac{3}{(-10.094)^{2}}$

$x_{3} = 0.971$

The values of $x_{1}$, $x_{2}$ and $x_{3}$ are 0.52, -10.094 and 0.971.

Answer 2

Answer:

=  0.52, -10.094 and 0.9705561461

Step-by-step explanation:

If you input this equation into a calculator while using brackets around $x$n, you should get these values above. Hope that helps!