Bunuel wrote:
A certain sequence is defined by the following rule: \(S_n = k(S_{n-1})\), where k is a constant. If S1 = 64 and S25 = 192, what is the value of S9 ?
(A) \(\sqrt{2}\)
(B) \(\sqrt{3}\)
(C) \(64\sqrt{3}\)
(D) \(64\sqrt[3]{3}\)
(E) \(64\sqrt[24]{3}\)
Kudos for a correct solution.
\(S_n = k(S_{n-1})\)
i.e. \(S_2 = k(S_{2-1}) = k(S_1)\)
and \(S_3 = k(S_{3-1}) = k(S_2) = k^2*(S_1)\)
and \(S_4 = k(S_{4-1}) = k(S_3) = k^3*(S_1)\)
and \(S_5 = k(S_{5-1}) = k(S_4) = k^4*(S_1)\)
...
...
and \(S_{25} = k(S_{25-1}) = k(S_24) = k^{24}*(S_1)\)
i.e. \(S_{25} = 192 = k^{24}*64\)
i.e. \(3 = k^{24}\)
i.e. \(3^{1/3} = k^8\)
Now, \(S_9 = k^8*(S_1) = 3^{1/3}*64\)
Answer: Option
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