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so I'm given a geometric series where \({t_1 = 6}\) and \({r = 1.5}\), where \({t_1}\) is the first term and \({r}\) is the common ratio.

i want to use the formula \(S_n = {t_1 ( 1 - r^{n}) \over 1 - r}\) where \({S_n}\) is the sum of the first \({n}\) terms and \({n}\) is the number of terms.

I want to find the sum for the first 10 terms. i plugged my numbers in and got the textbook answer of \({679.98}\) by doing bedmas on my calculator since there were big numbers.

the text also wants me to express my answer as an exact value in fraction form, how should i do that? the textbook answer is \({174 075 \over 256}\)

 Jul 6, 2018
edited by Guest  Jul 6, 2018
edited by Guest  Jul 6, 2018
 #1
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Sum=6 x [1 - 1.5^10] / [1 - 1.5]

Sum=6 x [1 -  57.665] / [-0.5]

Sum=6 x [-56.665] / [-0.5]

Sum =6 x   -56.6650390625 / - 0.5 

Sum =-339.990234375 / -0.5

 Jul 6, 2018
 #2
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the textbook answer is \({174075 \over 256}\) as the exact value in fraction form though :")

Guest Jul 6, 2018
 #3
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-339.990234375 / -0.5  x 512/512

174,075 / 256

 Jul 6, 2018

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