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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 ## 5 and 15 are the first tagged by: rolandprowess ##### This topic has 1 expert reply and 0 member replies ### Top Member ## 5 and 15 are the first 5 and 15 are the first two terms in a geometric sequence. What is the arithmetic difference between the 11th term and the 13th term? A. 3*5^2 B. 5* 3^13 - 5 * 3^11 C. 5^13 D. 40 * 3^10 E. 3^12 - 3^10 How will i start solving it? Can some experts help? OA D ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Quote: 5 and 15 are the first two terms in a geometric sequence. What is the arithmetic difference between the 11th term and the 13th term? A. 3*5^2 B. 5* 3^13 - 5 * 3^11 C. 5^13 D. 40 * 3^10 E. 3^12 - 3^10 How will i start solving it? Can some experts help? Hi lheiannie07, Let's take a look at your question. First two terms of geometric sequence are 5 and 15. $$a_1=5$$ $$a_2=15$$ We can find the common ratio by dividing the second term by first term. $$r=\frac{a_2}{a_1}=\frac{15}{5}=3$$ Now, we will find 11th term and 13th term of the geometric sequence. We know that nth term of a geometric sequence can be calculated using formula: $$a_n=a_1r^{n-1}$$ Therefore, 11th term will be: $$a_{11}=5.3^{11-1}$$ $$a_{11}=5.3^{10}$$ 13th term will be: $$a_{13}=5.3^{13-1}$$ $$a_{13}=5.3^{12}$$ In the question statement, we are asked to find the arithmetic difference between 11th and 13th term. $$a_{13}-a_{11}$$ $$=5.3^{12}-5.3^{10}$$ Factor out 5. $$=5\left(3^{12}-3^{10}\right)$$ Write 3^12 as 3^10*3^2 $$=5\left(3^{10}.3^2-3^{10}\right)$$ Factor out 3^10 $$=5.3^{10}\left(3^2-1\right)$$ $$=5.3^{10}\left(9-1\right)$$ $$=5.3^{10}\left(8\right)$$ $$=40.3^{10}$$ 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 GMAT Exam Know how you'd score today for$0

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