SOLUTION: An infinite geometric series has first term 70 and common ratio -0.23. To 2 decimal places, what is the sum to infinity of this series?

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Question 982715: An infinite geometric series has first term 70 and common ratio -0.23.
To 2 decimal places, what is the sum to infinity of this series?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
For a geometric sequence with first term b%5B1%5D and common ratio r ,
the sum of the first n terms is


When r%3C1 , r%5En gets progressively smaller as n increases, approaching zero,
so the sum of an infinite geometric series with first term b%5B1%5D and common ratio r%3C1 is
S=b%5B1%5D%2A%281%2F%281-r%29%29
In this case,
S=70%2A%281%2F%281-%28-0.23%29%29%29=70%2F%281%2B0.23%29=70%2F1.23=highlight%2856.91%29 rounded to two decimal places.