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

ans is D. I agree with the solution given above.

Regards,
Kapil