Question

9: A post is being driven into the ground. The first strike drives the post 25 inches into the ground. Each additional strike drives the stake 4/5 the distance further into the ground than the previous strike. What is the total distance (to the nearest inch) than the post is driven into the ground after 7 strikes?

Answer 1

Answer:

99

Explanation:

First strike=25 in

Second strike=4/5*25=20 in

Third strike=4/5*20=16 in

Fourth strike=4/5*16=12.8 in

Fifth strike=4/5*12.8=10.24 in

sixth strike=4/5*10.24=8.192 in

seventh strike=4/5*8.192=6.5536 in

Total=(25+20+16+12.8+10.24+8.192+6.5536) in=98.7856 in

Taking this as a geometric series

$Sum(7)=a\frac{(1-r^{7}}{1-r}$ where a is initial value taken as 25 for this case and r is rate taken as 4/5 or 0.8 in our case

$Sum(7)=25\frac {1-0.8^{7}}{1-0.8}=98.7856 in$

To the nearest inches, sum is 99 in