KPI Succession
==============

Let's consider the recursive definition of a mathematical succession parameterized by the real number constants :math:`a`, :math:`b`, and :math:`k`:

     :math:`x_{1} = a`

     :math:`x_{2} = b`

     :math:`x_{i+1} =  \frac {k \pi} {1+\sqrt{ {x_i}² + {x_{i-1}}² } }`

Implement the following two Python functions (following the order is recommended) in the module :mod:`kpi_module` (file :file:`kpi_module.py`).

The first function is:

    .. py:function:: kpi_next_term(x1, x2, k)

such that

    **given** ``x1``,  ``x2``, ``k`` :class:`float` values, where ``x1``,  ``x2``, are the values for two consecutive terms, and ``k`` is the parameter of our succession

    **returns**  a :class:`float` with the next term of the succession according to the above definition

For exemple:

   .. literalinclude:: kpi_next_term.test
      :language: python3
      :start-after: --ini
      :end-before: --fi
      
.. note:: Python standard modules such as :mod:`math` **may** be imported and used.

Doctests are available at the :download:`kpi_next_term.test` file.


The second function is:

    ``kpi_term5``:math:`(x_1, x_2, k)`

such that

    **given**
        | takes :math:`x_1, x_2`, :class:`float` values being the first and second terms of the succession respectively
        | returns a :class:`float` with the 5th term of the above succession. The float is rounded to 2 decimals.

For exemple:

   .. literalinclude:: kpi_term5.test
      :language: python3
      :start-after: --ini
      :end-before: --fi
      
.. note:: This function implementation **must** call the previous function as many times as needed.

Doctests for validation are available at the :download:`kpi_term5.test` file.