First series: the terms are generated by dividing alternatively by -2 then 2:
4/3÷(-2)=-2/3, -2/3÷2=-1/3, -1/3÷(-2)=1/6, 1/6÷2=1/12, 1/12÷(-2)=-1/24, -1/24÷2=-1/48, ...
Second series: reverse Fibonacci: subtract the second term from the first to get the next:
24/4-15/4=9/4, 15/4-9/4=6/4, 9-6/4=3/4, 6/4-3/4=3/4, 3/4-3/4=0 (the term 6/4, or 3/2, appears to be missing).
Third series: starting by subtracting 3/2 from the first time and doubling this to 3, then 6, and so on, we get successive terms: -5/2-3/2=-4, -4-3=-7, -7-6=-13, -13-12=-25, -25-24=-49, ...
Fourth series: geometric with common ratio -3/2, that is, each successive term is -3/2 times the previous term.
Fifth series: to get the next term, invert the fraction and add 1 to the numerator and denominator. I think the series should be:
3/7(→7/3)→8/4(→4/8)→5/9(→9/5)→10/6 (5/3)
(→6/10)→7/11(→11/7)→12/8 (not 12/18)(→8/12)→9/13
Sixth series: the difference between terms starts at 12, then increases by 20 to 32, 52, 72, making the next term 198+92=290 not 2810.