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# The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4

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The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4  [#permalink]

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11 Jul 2018, 01:12
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Difficulty:

35% (medium)

Question Stats:

71% (01:44) correct 29% (02:46) wrong based on 35 sessions

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[GMAT math practice question]

The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 - A3 = 10. Which of the following could be the formula for An+1 - An, in terms of n?

$$A. n + 1$$
$$B. n^2 + 1$$
$$C. n^2 - 1$$
$$D. n - 1$$
$$E. n^2 + 3$$

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" RC Moderator Status: Perfecting myself for GMAT Joined: 22 May 2017 Posts: 620 Concentration: Nonprofit Schools: Haas '21 GPA: 4 WE: Engineering (Computer Software) Re: The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 [#permalink] ### Show Tags 11 Jul 2018, 02:01 Solving by substitution Given $$A_{3}-A_{2} = 5$$ Above equation is of the form $$A_{n+1} - A_{n}$$ with n = 2 Choice A = > $$n+1 = 2+1 = 3\neq5$$ Wrong Choice B = > $$n^2+1 = 4+1 = 5\neq5$$ Probably correct Choice C = > $$n^2-1 = 4-1 = 3\neq5$$ Wrong Choice D = > $$n-1 = 2-1 = 1\neq5$$ Wrong Choice E = > $$n^2+3 = 4+3 = 7\neq5$$ Wrong Hence option B _________________ If you like my post press kudos +1 New - RC Butler - 2 RC's everyday Tag me in RC questions if you need help. Please provide your analysis of the question in the post along with the tag. Senior Manager Joined: 04 Aug 2010 Posts: 272 Schools: Dartmouth College Re: The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 [#permalink] ### Show Tags 11 Jul 2018, 03:03 MathRevolution wrote: [GMAT math practice question] The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 - A3 = 10. Which of the following could be the formula for An+1 - An, in terms of n? $$A. n + 1$$ $$B. n^2 + 1$$ $$C. n^2 - 1$$ $$D. n - 1$$ $$E. n^2 + 3$$ Let n=3. According to the blue portion above, An+1 - An = A4 - A3 = 10. The correct answer must yield a result of 10 when n=3. Only B works: n² + 1 = 3² + 1 = 10. _________________ GMAT and GRE Tutor Over 1800 followers Click here to learn more GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6212 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 [#permalink] ### Show Tags 15 Jul 2018, 07:01 => We try each possibility until we find a formula that works. A): If An+1 - An = n + 1, then A2 - A1 = $$1 + 1 = 2$$, which is correct, but A3 - A2 = $$2 + 1 = 3 ≠ 5.$$ So, A) is not the answer. B): If An+1 - An = $$n^2 +$$1, then A2 - A1 = $$1^2 + 1 = 2,$$ A3 - A2 =$$2^2 + 1 = 5,$$ A4 - A3 = $$3^2 + 1 = 10.$$ So, this formula is possible. Therefore, the answer is B. Answer: B _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: The terms of the sequence {An} satisfy A2 - A1 = 2, A3 - A2 = 5 and A4 &nbs [#permalink] 15 Jul 2018, 07:01
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