Numerical series
================

Save all functions into a file named ``numerical_series.py``.

A. A numerical series is defined as:

   :math:`x_1 = 1`

   :math:`x_{i} = \begin{cases} 
   x_{i-1} + 5 , & \mbox{if }   i-1    \mbox{ is even}  \\
   2x_{i-1} , & \mbox{if } i-1 \mbox{ is odd} \\ 
   \end{cases}`

   1. Write the function :py:func:`even_odd_1` that given an
   integer *n*, returns the average of the *n* first values of the
   defined numerical series. Examples:

      .. literalinclude:: even_odd_1.txt
         :language: python3
         :lines: 3-

      .. note::
        More tests are provided in file :download:`even_odd_1.txt <even_odd_1.txt>`

   2. Write the function :py:func:`even_odd_2` that given a
   value *xmax*, returns the average of the values of the defined
   numerical series, lower than *xmax*. Example:
   
      .. literalinclude:: even_odd_2.txt
         :language: python3
         :lines: 3-

   .. note::
        More tests are provided in file :download:`even_odd_2.txt <even_odd_2.txt>`


B. Given two integers *a* and *b*, such that *a>0* and *0< b< 10*, the
   following numerical series is defined:

   :math:`x_1 = a`

   :math:`x_i = \begin{cases} 
   2x_{i-1}, & \mbox{if }   x_{i-1} \mbox{ is multiple of b or its last digit is b} \\
   3x_{i-1} +b, & \mbox{if } x_{i-1} \mbox{ is not multiple of b and its last digit is not b}\\
   \end{cases}`

   1. Write the function :py:func:`sum_terms_1` that takes the values of
   ``a``, ``b`` and ``n``, and returns the addition of the ``n`` first
   terms of the given numerical series Examples:

   .. literalinclude:: sum_terms_1.txt
         :language: python3
         :lines: 3-

   .. note::
        More tests are provided in file :download:`sum_terms_1.txt <sum_terms_1.txt>`

   2. Write the function :py:func:`sum_terms_2` that takes the values of
      ``a``, ``b`` and ``xmax``, and returns the addition of the terms of
      the given numerical series, lower than ``xmax``. Examples:

      .. literalinclude:: sum_terms_2.txt
         :language: python3
         :lines: 3-

      .. note::
          More tests are provided in file :download:`sum_terms_2.txt <sum_terms_2.txt>`

.. rubric:: Solution

A solution of these functions is provided in file :download:`numerical_series.py <solutions/numerical_series.py>`