What should be the next number in the following series 100, 96, 104, 88, 120, 56?

The given series is: 100, 96, 104, 88, 120, 56.

To determine the next number, let’s examine the pattern in the series:

• From 100 to 96, the difference is -4.
• From 96 to 104, the difference is +8.
• From 104 to 88, the difference is -16.
• From 88 to 120, the difference is +32.
• From 120 to 56, the difference is -64.

We can see an alternating pattern of subtraction and addition with the differences being powers of 2:

• -4 (which is -2²)
• +8 (which is +2³)
• -16 (which is -2⁴)
• +32 (which is +2⁵)
• -64 (which is -2⁶)

If we follow this pattern, the next step should involve adding +128 (which is +2⁷) to the last number in the series:

56 + 128 = 184.

Therefore, the next number in the series should be 184.