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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
Joined: 16 Aug 2015
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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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00:00

Difficulty:

35% (medium)

Question Stats:

69% (02:03) correct 31% (02:16) wrong based on 101 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 $79 for 1 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: 359 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: 268 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 1 $$a_n$$ = $$a_{n-1}$$ + $$a_{n-2}$$ ....+ $$a_1$$ ----------------------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: 88 Re: There is a sequence an for a positive integer such that a3=a1+a2, a4= [#permalink] ### Show Tags 13 Jan 2017, 04:28 1 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: 268 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: 8017 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$79 for 1 month Online Course"
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Senior Manager
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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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27 Jan 2019, 16:59
Hello everyone!

Could anyone know where can I find more exercises like this one?

It has been really difficult for me when I have to decipher the terms represented with letters.

Thank you so much in advance!
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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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27 Jan 2019, 17:25
jfranciscocuencag wrote:
Hello everyone!

Could anyone know where can I find more exercises like this one?

It has been really difficult for me when I have to decipher the terms represented with letters.

Thank you so much in advance!

Hey jfranciscocuencag,

You can filter out for the type sequences in the link below.

https://gmatclub.com/forum/search.php?v ... s&style=11

Hope it helps.

Posted from my mobile device
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Senior Manager
Joined: 12 Sep 2017
Posts: 302
Re: There is a sequence an for a positive integer such that a3=a1+a2, a4=  [#permalink]

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27 Jan 2019, 17:29
Afc0892 wrote:
jfranciscocuencag wrote:
Hello everyone!

Could anyone know where can I find more exercises like this one?

It has been really difficult for me when I have to decipher the terms represented with letters.

Thank you so much in advance!

Hey jfranciscocuencag,

You can filter out for the type sequences in the link below.

https://gmatclub.com/forum/search.php?v ... s&style=11

Hope it helps.

Posted from my mobile device

Thank you Afc0892 !
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Posts: 906
Re: There is a sequence an for a positive integer such that a3=a1+a2, a4=  [#permalink]

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18 Mar 2019, 05:30
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 )

Hence option B.

Thank you, nice solution!
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Re: There is a sequence an for a positive integer such that a3=a1+a2, a4=   [#permalink] 18 Mar 2019, 05:30
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