Series
======

Let's consider the following mathematical succession parameterized by the real number constant :math:`a`:

    .. math:: x_{i+1}  = \frac{-1^{i+1} a sin(x_i)}{x_i/2}

Implement the following two Python functions (following the order is recommended) in the module :mod:`series12` (file :file:`series12.py`).

The first function is:

    ``calc_term``:math:`(a, i, x_i)`
        | takes 
        | :math:`a`, :class:`float` value,
        | :math:`i`, positive :class:`int` value,
        | :math:`x_i`, :class:`float` value representing an angle expressed in radians
        | returns
        | :math:`x_{i+1}` according to the above definition, as a :class:`float` value rounded to 4 decimals.

For exemple:

   .. literalinclude:: calc_term-test.txt
      :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:`calc_term-test.txt` file.


The second function is:

    ``sum4terms``:math:`(a, x_0)`
        | takes :math:`a, x_0`, :class:`float` values where :math:`x_0` is the first term of the succession
        | returns a :class:`float` with the addition of the first 4 terms of the above succession, being :math:`x_0` the first of them. The float is rounded to 2 decimals.

For exemple:

   .. literalinclude:: sum4terms-test.txt
      :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:`sum4terms-test.txt` file.