Bunuel wrote:

An "alpha series" is defined by the rule: \(A_n = A_{n - 1}*k\), where k is a constant. If the 1st term of a particular "alpha series" is 64 and the 25th term is 192, what is the 9th term?

A. \(\sqrt[24]{3}\)

B. \(\sqrt[24]{3^9}\)

C. \(64*\sqrt[24]{3^9}\)

D. \(64*\sqrt[3]{3}\)

E. \(64*\sqrt[3]{3^9}\)

As per the given rule for alpha series, it is a geometric progression.

1st term = 64

25th term = \(192 = 64 * k^{24}\)

\(k^{24} = 3\)

We need to find the 9th term i.e. \(64*k^8\)

\(k^8\) is cube root of \(k^{24}\) so it is cube root of 3. So 9th term is 64*cube root of 3

Answer (D)

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Karishma

Veritas Prep GMAT Instructor

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