A B C D E F G H
-1 -1 -5 -8 -5 9 39 Z
0 -4 -3 3 14 30 Y
-4 1 6 11 16 X
Interesting complexity here. The numbers in row one change by the addition of the numbers in row two.
Step AB is made by adding the first number in row two the the first number in row one: -1 + 0 = -1
Step BC is made by adding the second number in row two to the second number in row one: -1 + -4 = -5
For each number in row one, add the number that follows it in row two.
-5 + -3 = -8
-8 + 3 = -5
-5 + 14 = 9
9 + 30 = 39
39 + Y = Z
To get Y, the last number in row 2, we need the numbers in row 3. Follow the same steps.
0 + -4 = -4
-4 + 1 = -3
-3 + 6 = 3
3 + 11 = 14
14 + 16 = 30
30 + X = Y
If we can find X, we will know Y; if we know Y we can determine Z.
Notice that the numbers in row three increment by five. Therefore, X = 16 + 5 = 21
With X = 21, we get Y = 30 + X = 51
We finish with Z = 39 + Y = 90
The eigth number in the sequence is 90.