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The sequence (GMAT PREP 1)

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The sequence (GMAT PREP 1)

by alex.gellatly » Sun Sep 09, 2012 12:19 am
The sequence a1, a2, a3,.....,an of n integers is such that ak=k if k is odd and ak= -a(k-1) if k s even. Is the sum of the terms in the sequence positive?
1. n is odd
2. an is positive

Please note: any number or equation after a is supposed to be a subset. I don't know how to type subset here. I apologize for the inconvenience.

Thanks
A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231
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by neelgandham » Sun Sep 09, 2012 1:04 am
The sequence a1, a2, a3,.....,an of n integers is such that ak=k if k is odd and ak= -a(k-1) if k s even. Is the sum of the terms in the sequence positive?
The sequence is 1, -1, 3, -3, 5, -5, 7 -7...
So, if the number of terms in the sequence is odd(say 3), then the sum of the terms is positive (1-1+3= 3)
and if the number of terms in the sequence is even(say $), then the sum of the terms is 0 (1-1+3-3 = 0)
You can also observe that all the odd terms are positive and the even terms negative
1. n is odd
If n is odd, then the sum of the terms is positive.
e.g.If n = 3,Sum = 1 - 1 + 3 = 3
If n = 5,Sum = 1 -1 + 3 - 3 + 5 = 5
2. an is positive
If An is positive, n is odd. and If n is odd, then the sum of the terms is positive.

IMO D
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by KapilKapoor » Sun Sep 09, 2012 8:20 am
ans is D. I agree with the solution given above.

Regards,
Kapil
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