0, 1, - 3, 7, - 15, 31. What is the 100th number

0, 1, - 3, 7, - 15, 31. What is the 100th number

Absolute value of 1 = 0 + 1
-3 = - (absolute value of 1 + 2)
7 = (- 3) absolute value + 4
-15 = - (absolute value of 7 + 8)
31 = (- 15) absolute value + 16
.,
therefore
The 100th number
=The 98th power of 0 + 1 + 2 + 4 + 8 + 16 +... + 2
=The 98th power of 1 + 2 + 4 + 8 + 16 +... + 2
=(99th power of 1-2) / (1-2)
=The 99th power of 2 - 1