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An infinite geometric series has common ratio 1/3 and sum 25. What is the second term of the sequence?

 Jan 25, 2021
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S∞  = a1 / (1-r)

 25 = a1 /(1-1/3)

25 * 3/2 = a1   = 37.5    Not possible (already greater than the sum)       ratio must be   MINUS 1/3

 

S = a1/(1 - -1/3)

25 * 3/4 = a1 = 75/4         75/4 (-1/3) = -75/12   is the second term   (- 6.25)

 Jan 25, 2021

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