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# For the infinite sequence a1, a2, ..., an, the value of an is the sum

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Math Expert
Joined: 02 Sep 2009
Posts: 43789
For the infinite sequence a1, a2, ..., an, the value of an is the sum [#permalink]

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16 Jan 2018, 23:15
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65% (hard)

Question Stats:

57% (01:05) correct 43% (02:29) wrong based on 30 sessions

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For the infinite sequence $$a_1$$, $$a_2$$, ..., $$a_n$$, the value of $$a_n$$ is the sum of all previous terms in the sequence from $$a_1$$ through $$a_{n−1}$$, inclusive. If $$a_n=x$$ and $$n>2$$, which of the following expresses $$a_{n+2}$$ in terms of x?

A. x+2

B. 2x

C. 3x

D. 4x

E. 8X
[Reveal] Spoiler: OA

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Re: For the infinite sequence a1, a2, ..., an, the value of an is the sum [#permalink]

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16 Jan 2018, 23:26
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D

an=x=a1+a2+...a(n-1)
a(n+1)=a1+a2+...+a(n-1)+an=x+x=2x
a(n+2)=a1+a2+...+a(n-1)+an+a(n+1)=x+x+2x=4x

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Re: For the infinite sequence a1, a2, ..., an, the value of an is the sum   [#permalink] 16 Jan 2018, 23:26
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