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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?"

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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=(8)/(27)
r=\frac{\sqrt[3]{8}}{\sqrt[3]{27}}=(2)/(3)

ANSWER

The constant rate is 2/3

User Alberto Rhuertas
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