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There is a sequence an for a positive integer such that a3=a1+a2, a4=

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Math Revolution GMAT Instructor
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There is a sequence an for a positive integer such that a3=a1+a2, a4=  [#permalink]

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13 Jan 2017, 01:51
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45% (medium)

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66% (02:10) correct 34% (02:38) wrong based on 73 sessions

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There is a sequence an for a positive integer such that a3=a1+a2, a4=a3+a2+a1, an =an-1+an-2+an-3+….+a2+a1. If an=p, an+2=?

A. 2p B. 4p C. 8p D. 16p E. 24p

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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" Senior Manager Joined: 13 Oct 2016 Posts: 367 GPA: 3.98 Re: There is a sequence an for a positive integer such that a3=a1+a2, a4= [#permalink] Show Tags 13 Jan 2017, 02:09 1 MathRevolution wrote: There is a sequence an for a positive integer such that a3=a1+a2, a4=a3+a2+a1, an =an-1+an-2+an-3+….+a2+a1. If an=p, an+2=? A. 2p B. 4p C. 8p D. 16p E. 24p $$a_{n+2} = a_1 + a_2 + a_3 + ... + a_{n-1} + a_n + a_{n+1} = a_n + a_n + (a_n + a_n) = 4a_n = 4p$$ B. Senior Manager Joined: 19 Apr 2016 Posts: 274 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) There is a sequence an for a positive integer such that a3=a1+a2, a4= [#permalink] Show Tags Updated on: 13 Jan 2017, 05:42 $$a_n$$ = $$a_{n-1}$$ + $$a_{n-2}$$ ....+ $$a_1$$ ----------------------1 $$a_{n+1}$$ = $$a_{n}$$ + $$a_{n-1}$$ ....+ $$a_1$$ =$$a_{n}$$ + $$a_{n}$$ ----------------------2 $$a_{n+2}$$ = $$a_{n+1}$$ + $$a_{n}$$+ $$a_{n-1}$$ + .... + $$a_1$$ ----------------------3 $$a_{n+2}$$ = $$a_{n}$$ + $$a_{n}$$ + $$a_{n}$$ + $$a_{n}$$ = 4$$a_{n}$$ = 4p ( by using st. 1,2 and 3 ) Hence option B. Originally posted by 0akshay0 on 13 Jan 2017, 02:26. Last edited by 0akshay0 on 13 Jan 2017, 05:42, edited 1 time in total. Manager Joined: 13 Apr 2010 Posts: 89 Re: There is a sequence an for a positive integer such that a3=a1+a2, a4= [#permalink] Show Tags 13 Jan 2017, 04:28 0akshay0 wrote: $$a_n$$ = $$a_{n-1}$$ + $$a_{n-2}$$ ....+ $$a_1$$ ----------------------1 $$a_{n+1}$$ = $$a_{n}$$ + $$a_{n-1}$$ ....+ $$a_1$$ =$$a_{n}$$ + $$a_{n}$$ ----------------------2 $$a_{n+2}$$ = $$a_{n+1}$$ + $$a_{n}$$+ $$a_{n-1}$$ + .... + $$a_1$$ ----------------------3 $$a_{n+2}$$ = $$a_{n}$$ + $$a_{n}$$ + $$a_{n}$$ + $$a_{n}$$ = 4$$a_{n}$$ = 4p ( by using st. 1,2 and 3 ) Question is asking what is $$a_{n+2}$$ Given $$a_n$$ = $$a_{n-1}$$ + $$a_{n-2}$$+$$a_{n-3}$$...........+ $$a_1$$ = p $$a_{n+1}$$ = $$a_n$$ + $$a_{n-1}$$ + $$a_{n-2}$$+$$a_{n-3}$$........... + $$a_1$$ = p + p = 2p $$a_{n+2}$$ = $$a_{n+1}$$ + $$a_n$$ + $$a_{n-1}$$ + $$a_{n-2}$$+$$a_{n-3}$$........... + $$a_1$$ = 2p + p + p = 4p Answer is B Senior Manager Joined: 19 Apr 2016 Posts: 274 Location: India GMAT 1: 570 Q48 V22 GMAT 2: 640 Q49 V28 GPA: 3.5 WE: Web Development (Computer Software) There is a sequence an for a positive integer such that a3=a1+a2, a4= [#permalink] Show Tags 13 Jan 2017, 07:34 sb0541 wrote: 0akshay0 wrote: $$a_n$$ = $$a_{n-1}$$ + $$a_{n-2}$$ ....+ $$a_1$$ ----------------------1 $$a_{n+1}$$ = $$a_{n}$$ + $$a_{n-1}$$ ....+ $$a_1$$ =$$a_{n}$$ + $$a_{n}$$ ----------------------2 $$a_{n+2}$$ = $$a_{n+1}$$ + $$a_{n}$$+ $$a_{n-1}$$ + .... + $$a_1$$ ----------------------3 $$a_{n+2}$$ = $$a_{n}$$ + $$a_{n}$$ + $$a_{n}$$ + $$a_{n}$$ = 4$$a_{n}$$ = 4p ( by using st. 1,2 and 3 ) Question is asking what is $$a_{n+2}$$ Given $$a_n$$ = $$a_{n-1}$$ + $$a_{n-2}$$+$$a_{n-3}$$...........+ $$a_1$$ = p $$a_{n+1}$$ = $$a_n$$ + $$a_{n-1}$$ + $$a_{n-2}$$+$$a_{n-3}$$........... + $$a_1$$ = p + p = 2p $$a_{n+2}$$ = $$a_{n+1}$$ + $$a_n$$ + $$a_{n-1}$$ + $$a_{n-2}$$+$$a_{n-3}$$........... + $$a_1$$ = 2p + p + p = 4p Answer is B I did the same thing. St. 1,2 and 3 explains how $$a_{n+2}$$ = 4$$a_n$$ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6371 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: There is a sequence an for a positive integer such that a3=a1+a2, a4= [#permalink] Show Tags 15 Jan 2017, 18:45 ==> Since an =an-1+an-2+an-3+….+a2+a1 =p, an+1 =an+ an-1+an-2+an-3+….+a2+a1=p+p=2p an+2=an+1+an+an-1+an-2+an-3+….+a2+a1=2p+p+p=4p. Hence, 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: There is a sequence an for a positive integer such that a3=a1+a2, a4=  [#permalink]

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30 Jul 2018, 00:51
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Re: There is a sequence an for a positive integer such that a3=a1+a2, a4= &nbs [#permalink] 30 Jul 2018, 00:51
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