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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 sequence is defined by the following rule: tagged by: VJesus12 ##### This topic has 1 expert reply and 0 member replies ### Top Member ## A certain sequence is defined by the following rule: A certain sequence is defined by the following rule: $$S_n=k(S_{n-1}),$$ where$k$is a constant. If $$S_1=64\ \ \ \ and\ \ \ \ \ S_{25}=192,$$ what is the value of $$S_9?$$ $$A.\ \ \ \sqrt{2}$$ $$B.\ \ \ \sqrt{3}$$ $$C.\ \ \ 64\sqrt{3}$$ $$D.\ \ \ 64\sqrt[3]{3}$$ $$E.\ \ \ 64\sqrt[24]{3}$$ Experts, how can I find the correct answer here? I need some help to solve this PS question. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: A certain sequence is defined by the following rule: $$S_n=k(S_{n-1}),$$ where$k$is a constant. If $$S_1=64\ \ \ \ and\ \ \ \ \ S_{25}=192,$$ what is the value of $$S_9?$$ $$A.\ \ \ \sqrt{2}$$ $$B.\ \ \ \sqrt{3}$$ $$C.\ \ \ 64\sqrt{3}$$ $$D.\ \ \ 64\sqrt[3]{3}$$ $$E.\ \ \ 64\sqrt[24]{3}$$ Experts, how can I find the correct answer here? I need some help to solve this PS question. Hi VJesus12, Lets take a look at your question. The sequence is defined by the rule: $$S_n=k(S_{n-1})$$ Then $$S_2=k(S_1)$$ $$S_3=k(S_2)=k(k(S_1))=k^2(S_1)$$ $$S_4=k(S_3)=k(k^2(S_1))=k^3(S_1)$$ $$S_5=k(S_4)=k(k^3(S_1))=k^4(S_1)$$ $$. . . . .$$ $$. . . . .$$ $$. . . . .$$ $$S_{25}=k(S_{24})=k(k^{23}(S_1))=k^{24}(S_1)$$ Therefore, we got a formula for S25, $$S_{25}=k^{24}(S_1)$$ Plugin the known values: $$192=k^{24}(64)$$ $$k^{24}=\frac{192}{64}=3$$ $$k^{\frac{24}{3}}=3^{\frac{1}{3}}$$ $$k^{8}=3^{\frac{1}{3}}$$ We are asked to find S9: $$S_9=k^{8}(S_1)$$ $$S_9=3^{\frac{1}{3}}(64)$$ $$S_9=64\sqrt[3]{3}$$ Therefore, Option D is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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