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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?"

Respuesta :

We have the

s(1)=27

s(4)=8

then we will have the next form

[tex]s(n)=s(1)(r)^{n-1}[/tex]

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

[tex]8=27(r)^3[/tex]

then we isolate the r that is the rate

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

ANSWER

The constant rate is 2/3

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