# What is the next number in the following sequence?

1, 6, 5, 3, 4, 1, 2, 2, ?

Hint: the task is pattern recognition using basic mathematical operations.

• Has a correct answer been given? If so, please don't forget to $\color{green}{\checkmark \small\text{Accept}}$ it :) – Rubio Oct 11 '17 at 14:32
• s this pattern the result of a series based on a starting rule that is then used to construct the rest of the series? Like a Fibonacci series? Or is this a pattern that you arbitrarily dreamed up according to a rule that cannot start a series? – – Dr t Oct 18 '17 at 18:14

I guess:

The answer is 0. Every third number is the difference between the previous 2 numbers.

• the only issue i take with an answer like this is, it breaks up the single sequence into individual sequences of 3 entries. However, I like the answer as it answers the question. – Jason V Oct 5 '17 at 13:53
• Is this pattern the result of a series based on a starting rule that is then used to construct the rest of the series? Like a Fibonacci series? Or is this a pattern that you arbitrarily dreamed up according to a rule that cannot start a series? – Dr t Oct 18 '17 at 18:13

If I have to solve this question, you can do this.

Subtract the first number from the second number. 6- 1 = 5, 4 - 3 = 1 , 2 - 2 = 0

so, the series would be

(1, 6, 5), (3, 4, 1), (2, 2, 0)...
Now after 0, the number would be 1.
Adding the triplets and dividing by 4, we get the next number.
See, (1 + 6 + 5)/4 = 3,
(3 + 4 + 1)/4 = 2,
(2 + 2 + 0)/4 = 1

so, the series now would be

(1, 6, 5), (3, 4, 1), (2, 2, 0), 1
And then the next number in the series would be 0
Check the middle number of the triplets, it decreases by 2.
6, 4, 2 and then comes 0

so, the series would be

(1, 6, 5), (3, 4, 1), (2, 2, 0), (1, 0, -1), (0, -2, -2), .........