SOLUTION: A pile driver drives a post 9 feet into the ground on its first hit. Each additional hit drives the post 2/3 the distance of the prior hit. a) find the total distance the post ha

Algebra ->  Sequences-and-series -> SOLUTION: A pile driver drives a post 9 feet into the ground on its first hit. Each additional hit drives the post 2/3 the distance of the prior hit. a) find the total distance the post ha      Log On


   

Question 447635: A pile driver drives a post 9 feet into the ground on its first hit. Each additional hit drives the post 2/3 the distance of the prior hit.
a) find the total distance the post has been driven after 4 hits.
b) what is the greatest distance the pole could be driven into the ground?
If you could help me with this problem, I would really appreciate it. Thanks.
Found 2 solutions by solver91311, edjones:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


First hit: .

Second hit:

Third hit:

Fourth hit:

In general: -th hit:


John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
a)
9+6+4+ 8/3 = 65'/3 Easier than using the formula S[n}=a[1]((1-r^n)/(1-r)) where r=2/3, n=4, a[1]=9
.
b)
S=a[1]/(1-r)=9/(1-(2/3))
=9/(1/3)
=27'
.
Ed