Question

Hi, I am beginning to apply Arithmetic and Geometric Sequences into world problems and I seem to be stumped on this last question. "A pile driver drives a post 27 inches on its first hit and 8 inches on its fourth hit. The depth of the driver after each additional hit is a constant rate. What is the value of this rate?"

Answer 1

We have the

s(1)=27

s(4)=8

then we will have the next form

$s(n)=s(1)(r)^{n-1}$

we know s(1) and s(4) so we will substitute

$8=27(r)^3$

then we isolate the r that is the rate

$r^3=\frac{8}{27}$$r=\frac{\sqrt[3]{8}}{\sqrt[3]{27}}=\frac{2}{3}$

ANSWER

The constant rate is 2/3