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# The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If

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Math Revolution GMAT Instructor
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The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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25 Sep 2018, 03:42
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45% (medium)

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70% (01:53) correct 30% (02:04) wrong based on 104 sessions

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[Math Revolution GMAT math practice question]

The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If n is a positive integer, what could be the value of Sn-Sn-1 in terms of n?

$$A. n$$
$$B. n^2$$
$$C. –n$$
$$D. -n^2$$
$$E. (n-1)^2$$

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"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Intern Joined: 17 May 2018 Posts: 49 Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If [#permalink] ### Show Tags 25 Sep 2018, 04:09 We see that the increment in the given sequence is: From S1 to S2: +1 = 1^2 From S2 to S3: +4 = 2^2 From S3 to S4: +9 = 3^2 From S4 to S5: +16 = 4^2 ... Thus from Sn-1 to Sn = (n-1)^2. Answer E _________________ ¿Tienes que presentar el GMAT y no sabes por dónde empezar? ¡Visita GMAT para Principiantes y recibe el curso completo gratis! CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2931 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If [#permalink] ### Show Tags 25 Sep 2018, 05:30 MathRevolution wrote: [Math Revolution GMAT math practice question] The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If n is a positive integer, what could be the value of Sn-Sn-1 in terms of n? $$A. n$$ $$B. n^2$$ $$C. –n$$ $$D. -n^2$$ $$E. (n-1)^2$$ To answer any question of sequences, one needs to find a pattern so we keep looking at what we get when we canculate expressions like $$S_n - S_{n-1}$$ $$S_1 = 1$$ $$S_2 = 2$$ i.e. $$S_2 - S_{1} = 1= 1^1$$ $$S_3 = 6$$ i.e. $$S_3 - S_{2} = 4 = 2^2$$ $$S_4 = 15$$ i.e. $$S_4 - S_{3} = 9 = 3^2$$ i.e. $$S_n - S_{n-1} = (n-1)^2$$ Answer: Option E _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION CEO Joined: 12 Sep 2015 Posts: 3717 Location: Canada Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If [#permalink] ### Show Tags 25 Sep 2018, 09:57 3 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If n is a positive integer, what could be the value of Sn-Sn-1 in terms of n? $$A. n$$ $$B. n^2$$ $$C. –n$$ $$D. -n^2$$ $$E. (n-1)^2$$ If you don't spot a pattern, you can always TEST the answer choices We want to find Sn - Sn-1 So, let's test a value of n. How about n = 2 So, we want to find the value of S2 - S1 Well, we're told that S2 = 2 and S1 = 1 So, S2 - S1 = 2 - 1 = 1 So, when n = 2, the answer to the question (what is the value of Sn - Sn-1) is 1 Now we'll check the answer choices to see which one yields an OUTPUT of 1 when we input n = 2 A. n = 2. NO GOOD. We need an output of 1. ELIMINATE B. n² = 2² = 4. NO GOOD. We need an output of 1. ELIMINATE C. -n = -2 = -2. NO GOOD. We need an output of 1. ELIMINATE D. -n² = -2² = -4. NO GOOD. We need an output of 1. ELIMINATE E. (n - 1)² = (2 - 1)² = 1. perfect!! Answer: E Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7352 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If [#permalink] ### Show Tags 27 Sep 2018, 00:56 => We begin by writing out the terms of the sequence: S2-S1 $$= 2 -1 = 1=1^2$$ S3-S2 $$= 6 – 2 = 4 = 2^2$$ S4-S3 $$= 15 – 6 = 9 = 3^2$$ S5-S4 $$= 31-15 = 16 = 4^2$$ Following the above pattern gives Sn-Sn-1 $$= (n-1)^2$$ Therefore, the answer is E. Answer: E _________________ 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$149 for 3 month Online Course"
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Joined: 12 Sep 2017
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The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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24 Jan 2019, 18:35
Hello everyone!

Just to clarify.

Sn-Sn-1 $$= (n-1)^2$$

n = The position of the term, right?

I am getting confused with the symbols.

Kind regards!
VP
Joined: 09 Mar 2018
Posts: 1004
Location: India
Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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24 Jan 2019, 20:49
1
jfranciscocuencag wrote:
Hello everyone!

Just to clarify.

Sn-Sn-1 $$= (n-1)^2$$

n = The position of the term, right?

I am getting confused with the symbols.

Kind regards!

I would like to pitch in here.

Yes are correct, n is indeed the position of the term, because n is a positive integer and it is a part of this series.

s1 = 1, s2 = 2, s3= 6 ...

s2 = s2 - s1 = 1, 2-1 = 1^2

s3 = s3 - s2 = 6-2 = 4, which is nothing but (n-1)^2, (3-1)^2 = 4

Here n is the position of the integer in the series.

Kindly let me know if this helps.
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Joined: 16 Dec 2018
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Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If  [#permalink]

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25 Jan 2019, 02:08
Ans is E.if u have problem with logic. Ucan just substute n =2 in ans

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Re: The sequence Sn has the terms S1=1, S2=2, S3=6, S4=15, S5=31, ……. If   [#permalink] 25 Jan 2019, 02:08
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