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# In a certain sequence a1, a2, ...an..., for n>1, each term is the sum

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Manager
Joined: 30 May 2018
Posts: 88
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
In a certain sequence a1, a2, ...an..., for n>1, each term is the sum  [#permalink]

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06 Apr 2019, 22:22
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Difficulty:

65% (hard)

Question Stats:

52% (01:58) correct 48% (01:55) wrong based on 63 sessions

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In a certain sequence a1, a2, ...an..., for n>1, each term is the sum of all previous terms. If an=S, in terms of S, a(n+3)=?

(A) 3S
(B) 4S
(C) 6S
(D) 8S
(E) 9S
Manager
Joined: 21 Feb 2019
Posts: 124
Location: Italy
Re: In a certain sequence a1, a2, ...an..., for n>1, each term is the sum  [#permalink]

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07 Apr 2019, 16:34
2
$$a_n = S$$
$$a_{n+1} = S + S = 2S$$
$$a_{n+2} = 2S + 2S = 4S$$
$$a_{n+3} = 4S + 4S = 8S$$
Intern
Joined: 18 Jan 2019
Posts: 28
Re: In a certain sequence a1, a2, ...an..., for n>1, each term is the sum  [#permalink]

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22 Apr 2019, 01:02
lucajava wrote:
$$a_n = S$$
$$a_{n+1} = S + S = 2S$$
$$a_{n+2} = 2S + 2S = 4S$$
$$a_{n+3} = 4S + 4S = 8S$$

can you explain the logic behind this?
Manager
Joined: 21 Feb 2019
Posts: 124
Location: Italy
Re: In a certain sequence a1, a2, ...an..., for n>1, each term is the sum  [#permalink]

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22 Apr 2019, 01:45
1
Ish1996 each term is the sum of all previous terms, so if $$a_n = S$$, $$a_{n+1}$$ is equal to all previous terms of $$a_n$$, which give S as result, in addition to $$a_n$$ itself, which is S.
Repeat this reasoning for the following ones and you will get the correct answer.

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Re: In a certain sequence a1, a2, ...an..., for n>1, each term is the sum   [#permalink] 22 Apr 2019, 01:45
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