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Math Revolution GMAT Instructor V
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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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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.
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$$a_n$$ = $$a_{n-1}$$ + $$a_{n-2}$$ ....+ $$a_1$$ ----------------------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.
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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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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

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

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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

I did the same thing.
St. 1,2 and 3 explains how $$a_{n+2}$$ = 4$$a_n$$ Math Revolution GMAT Instructor V
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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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==> 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.
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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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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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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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Re: There is a sequence an for a positive integer such that a3=a1+a2, a4=  [#permalink]

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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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Re: There is a sequence an for a positive integer such that a3=a1+a2, a4=  [#permalink]

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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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- Stne 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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