Alternate Distance 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} =  (-1)^{i+1} \frac{1+\sqrt{ {x_i}² + {x_{i-1}}² } }{2} \pi`

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

The first function is:

    .. py:function:: adist_term(xim1, xi, i)

such that

    **given** ``xim1``,  ``xi`` :class:`float` values, where ``xim1``,  ``xi``, are the values for two consecutive terms of our succession, and ``i`` is an :class:`int` index of ``xi``

    **returns**  a :class:`float` with the term ``i+1`` of the succession above

For exemple:

   .. literalinclude:: adist_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:`adist_term.test` file.

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The second function is:

    .. py:function:: adist_t4t5(a, b)

such that

    **given** ``a``, ``b``, :class:`float` values being the 1st and 2nd terms of the succession respectively

    **returns** a :class:`float` with the addition of the 4th and the 5th terms of the  succession above. The float is rounded to 4 decimals.

For exemple:

   .. literalinclude:: adist_t4t5.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:`adist_t4t5.test` file.