The sequence a1, a2 ,a3...,an of n integers is such that ak=k if k is odd and ak=-(ak-1) if k is even. Is the sum of the terms in the sequence positive?

A-- n is odd.

B-- an is positive..








if you just follow the formula, you arrive at
a1 = 1
a2 = -1
a3 = 3
a4 = -3
a5 = 5
etc
the pattern is pretty obvious.

and the SUMS of the terms are**
sum1 = 1
sum2 = 0
sum3 = 3
sum4 = 0
sum5 = 5
etc
this pattern is also pretty obvious (it's n if n is odd, and 0 if n is even).

based on this pattern recognition, we can realize that the question can be rephrased as, is n odd?

--

statement (1)
sufficient

statement (2)
notice that the positive terms are exactly those for which n is odd, so this statement is basically telling us that n is odd.
sufficient

ans = d