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# geometric series

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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 24, 2021

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Let S be the sum and a is the first term:

S = S/5 + a = 16

5S = S + 5a = 80

4S = 5a

4 x 16 = 5a

64 = 5a

a = $\boxed{\frac{64}5}$

Aug 24, 2021
edited by SparklingWater2  Aug 24, 2021