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# help

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Ariana just started a running plan where she runs 8 miles the first week and then increases the number of miles she runs by 5% each week. If she keeps up this plan for 9 weeks, how many total miles would Ariana have run, to the nearest whole number?

Apr 2, 2020

#1
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8   +   8(1.05)    + 8 (1.05)^2   + 8 (1.05)^3 ......8(1.05)^8

8 * $$\sum_{0}^{8}$$  1.05n      = 8 x 11.0265 =  ~~88.213 ~~ 88 miles     Edited: I made a typo   had 10.0265   should be 11.0265

Apr 2, 2020
edited by ElectricPavlov  Apr 2, 2020
#2
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Sum of GP = 8 * [1 - 1.05^9] / [1 - 1.05] =~88 miles

(8, 8.4, 8.82, 9.261, 9.72405, 10.2102525, 10.72076512, 11.25680338, 11.81964355) =88.2125... =~88 miles

Apr 2, 2020