Based on the data below which represents the approximations

Based on the data below which represents the approximations to a solution of some equation and assuming the algorithm used was either the method, ordinary fixed point iteration newton iteration or the secant method was most likely the method used ... and why?

Solution

The given data could be the result of secant iterations.

Reason: Except for secant method, in all other methods from the list, we get approximations on each side of the actual solution. But in secant method we can get more than 1 consecutive successive approximations on the same side of the actual solution.

Here from the table, we can see that results from first three iterations lie on the same side of the actual solution. Therefore, this data is the result of secant method.