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The sequence a(1), a(2), a(3), ... a(n) of n integers is suc

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The sequence a(1), a(2), a(3), ... a(n) of n integers is suc

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The sequence a(1), a(2), a(3), ... a(n) of n integers is such that a(k) = k if k is odd, and a(k) = -a(k-1) if k is even. Is the sum of the terms in the sequence positive?

(1) n is odd
(2) a(n) is positive

OA D

Source: GMAT Prep

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BTGmoderatorDC wrote:
The sequence a(1), a(2), a(3), ... a(n) of n integers is such that a(k) = k if k is odd, and a(k) = -a(k-1) if k is even. Is the sum of the terms in the sequence positive?

(1) n is odd
(2) a(n) is positive

OA D

Source: GMAT Prep
From the given information, we have

a(1) = 1;
a(2) = -a(1) = -1;
a(3) = 3;
a(4) = -a(3) = -3;
a(5) = 5;
a(6) = -a(5) = -5
...

We see that if the number terms is even, the sum of the terms = 0. Take for example, the sum of 1 + (-1) + 3 + (-3) = 0. However, if the number terms is odd, the sum of the terms = positive. Take for example, the sum of 1 + (-1) + 3 + (-3) + 5 = 5.

So, if are able to ascertain whether n is even or odd, we get the answer.

Let's take each statement one by one.

(1) n is odd.

Sufficient. The answer is Yes.

(2) a(n) is positive.

Since any term is positive when the term is odd, thus n is odd. Sufficient. The answer is Yes.

The correct answer: D

Hope this helps!

-Jay
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