a1, a2, a3, a4, a5..... aN

ak = k, if K is odd...
ak = -a(k-1) , if K is even...

that means

a1 = since k is odd... = 1,
a2 = since k is even..... a2 = -a(k-1)...-a(2-1)....-a(1).... =-1
a3 = 3
a4 = -3
a5 = 5
a6 =-5
and so on......

this sequence will always be positive if... it has odd number of terms
1+(-1)+3 = 3
1+(-1)+3+(-3)+5 = 5
and so on....

Statement A is sufficient

Also - if aN is positive...

that means the sequence stops at
a1 or a3 or a5 (see above) they all have positive values...
this also means that ... there are odd number terms in the sequence.. which we proved in statement 1 to be positive...

Statement B is sufficient too

IMO Answer should be "D"