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An infinite geometric series has a common ratio $-1/5$ and sum $16.$ What is the first term of the series?

 Aug 28, 2020
 #1
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From the forumla for an infinite geometric series, the first term is 28/5.

 Aug 28, 2020
 #2
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Sum = F / [1 - ( - 1/5)]

 

16 = F / (6/5)

16 = F x (5/6)

16 = 5F / 6      Cross multiply

5F = 16 * 6 = 96

F = 96 / 5 - which is the first term

 Aug 28, 2020

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