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?
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