Question

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

Answer 1

• The next number in the series 100, 96, 104, 88, 120, 56, ... is: 184

Step-by-step explanation:

1) You need to try to find a pattern in the given sequence, so that you can conclude a rule to determine each number in the sequence.

2) The first logical approach to find such pattern is to find the differences between any pair of consecutive numbers. That leads you to this:

• 96 - 100 = - 4

• 104 - 96 = 8

• 88 - 104 = - 16

• 120 - 88 = 32

• 56 - 120 = - 64

3) From that, you can see that the difference between two consecutive numbers is scaled by a factor of - 2. That is shown here:

• First difference = - 4

• Second difference = 8 = - 4 ( - 2)

• Third difference = - 16 = 8 (- 2)

• Fourth difference = 32 = - 16 ( - 2)

• Fifth difference = - 64 = 32 ( - 2)

4) Therefore, in words, the rule is "add (- 2) times the previous difference", which is:

• - 64 ( -2) = + 128

⇒ 56 + 128 = 184.

⇒ Answer: the next number is 184.