# How to determine convergence rate

An iterative method has been used to solve a non-linear equation f$$(x)=0$$. The table below show the iterations $$x_k$$ at $$k$$.

$$\begin{array}{c|c|} & \text{} & \text{} \\ \hline \text{k} & 0 &1&2&3&4 \\ \hline \text{x_k} & 1.2000 & 1.3000 & 1.3250 & 1.3313 &1.3329 \\ \hline \end{array}$$

What convergence rate does the method have?

Correct answer: $$p=1$$

How can you determine the convergence rate for a method like this? I know that linear convergence gives $$p=1$$ and quadratic convergence gives $$p=2$$. However, I am having a difficult time understanding how I can see whether data given follows a linear, quadratic or cubic convergence.

I would appreciate it if anyone could give me some guidelines on how to determine different convergence rates. Thank you!