Problem:
Find the sum of the following infinite geometric sequences 20, - 4, 4/5,...
Solution:
r = -4/20
r = -1/5
a1 = 20
[tex]\[\begin{array}{l}S = \frac{{{a_1}}}{{1 - r}}\\\\S = \frac{{20}}{{1 - ( - \frac{1}{5})}}\\\\S = \frac{{20}}{{1 + \frac{1}{5}}}\\\\S = \frac{{20}}{{\frac{6}{5}}}\\\\S = 20(\frac{5}{6})\\\\S = \frac{{100}}{6}\\\\S = \frac{{50}}{3}\\\\S = 16.667\end{array}\][/tex]
Answer:
Sum = 16.667
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