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100 points for 49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## A certain series is defined by the following recursive rule: ##### This topic has 1 expert reply and 1 member reply ### Top Member ## A certain series is defined by the following recursive rule: ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult A certain series is defined by the following recursive rule: Sn=K(Sn-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, wha is the 9th term? A. ROOT 2 B. ROOT 3 C. 64*ROOT 3 D. 64*3^1/3 E. 64*3^24 OA D Source: Manhattan Prep ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 965 messages Followed by: 4 members Top Reply \begin{align} S_n &= kS_{n-1} \\ S_{25} &= 192 = k S_{24} \\ &= k^{24}*64 \end{align} And $$S_{1} = 64 = k S_0$$ $$\Rightarrow k^{24} = \frac{192}{64} = 3 \quad \cdots \quad (1)$$ Now, $$S_9 = k^8 * 64$$ From $$(1)$$, $$(k^8)^3 = 3$$ $$k^8 = 3^{\frac{1}{3}}$$ $$S_9 = 3^{\frac{1}{3}} * 64$$ Therefore, answer __D__. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: A certain series is defined by the following recursive rule: Sn=K(Sn-1) , where k is a constant. If the 1st term of this series is 64 and the 25th term is 192, what is the 9th term? A. ROOT 2 B. ROOT 3 C. 64*ROOT 3 D. 64*3^1/3 E. 64*3^24 OA D Source: Manhattan Prep I'm not crazy about this question. Typically, when we talk about series, Sn represents the SUM of the first n terms of that series. However, based on the official answer, Sn seems to represent the value of TERM n. Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! • FREE GMAT Exam Know how you'd score today for0

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