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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 ## In the sequence S, the difference between . . . tagged by: Vincen ##### This topic has 2 expert replies and 1 member reply ### Top Member ## In the sequence S, the difference between . . . In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence? A. -4 B. 0 C. 4 D. 8 E. Cannot be Determined The OA is B. Why is B the correct answer? How can I determine this value? I need your help experts. Thanks. ### Top Member Master | Next Rank: 500 Posts Joined 15 Oct 2009 Posted: 330 messages Upvotes: 27 Vincen wrote: In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence? A. -4 B. 0 C. 4 D. 8 E. Cannot be Determined The OA is B. Why is B the correct answer? How can I determine this value? I need your help experts. Thanks. Call the first number in the sequence N. The problem states that consecutive terms differ by a constant amount, call it X. So the first number in the sequence is N. The second N+X and so on, with fourth term being N+3X, fifth being N+4X and seventh being N+6X. The problem states that the sum of fourth and fifth terms equals seventh term, so: (N+3X)+(N+4X) = N+6X simplifying 2N+7X=N+6X yields X=-N Looks strange but continue with that and substitute back into the second sequence term above N+X = N+(-N) = 0, B ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello Vincen. We have that the difference between any two consecutive terms is equal, that is to say, $$S=a,\ \ a+d,\ \ a+2d,\ \ a+3d,\ \ a+4d,\ \ a+5d,\ \ a+6d\ .\ .\ .\ .$$ Also we have that the sum of the fourth term and the fifth term of the sequence is equal to the seventh term, that is to say, $$\left(a+3d\right)+\left(a+4d\right)=a+6d\ \leftrightarrow\ 2a+7d=a+6d\ \leftrightarrow\ \ a=-d.$$ Replacing this value of "a" in the second term of the sequence we will get $$a+d=-d+d=0.$$ So, the correct answer is B. I hope this explanation may help you. I'm available if you'd like a follow up. Regards. _________________ 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 Vincen wrote: In the sequence S, the difference between any two consecutive terms is equal. If the sum of the fourth term and the fifth term of the sequence is equal to the seventh term of the sequence, what is the value of the second term of the sequence? A. -4 B. 0 C. 4 D. 8 E. Cannot be Determined We can let the first term = x. The second term is x + n. The 3rd is x + 2n. The 4th is x + 3n. The 5th is x + 4n. The 6th is x + 5n. The 7th is x + 6n. Thus: x + 3n + x + 4n = x + 6n 2x + 7n = x + 6n x = -n So, the 2nd term is -n + n = 0. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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