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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