precal
posted by Student .
A pile driver pounds a steel column into the ground. On the first drive, the column is pounded 1.65 metres into the ground, and on each successive drive it moves 80% as far as it did on the previous drive. The least number of drives required to drive the column a total of 8.2 metres into the ground is _____.

so you want
1.65 + 1.65(.8) + 1.65(.8)^2 + .. = 8.2
you could just keep adding until you reach 8.2 but that would be less elegant than using a geometric series
a = 1.65
r = .8
Sum(n) = 8.2
a(1  r^n)/(1r) = sum(n)
1.65(1  .8^n)/(1.8) = 8.2
(1.8^n)/.2 = 8.2/1.65
1.8^n = 8.2/1.65*.2
.8^n = 1  8.2/1.65*.2
n log .8 = log [1  8.2/1.65*.2]
n = log [1 8.2/1.65*.2] / log .8 = 22.8
22 drives will not do it, so they will need 23 pile drivings
check:
Sum(22) = 1.65 (1.8^22)/.2 = 8.189
sum(23) = 1.65(1.8^23)/.2 = 8.2013
my answer is correct.