Question 384316: Find the missing number: 5, 8, 6, 4, 4, 0, 8, ?
I tried 3n-1. I started with n=2,then n=3, but it failed at n=4.
I also tried the multiple of the difference of the numbers. the difference between 5&8 is 3, then multiply that by the difference between 8&6 which is 2; so (5-8)* (8-6)= 6. Then (8-6) * (6-4)=4, then (6-4) * (4-4)=0
That's where it failed.
I also tried 2n-1 starting with n=3, but that failed also.
I looked for a pattern in the difference between the numbers, like the triangular numbers or Fibonacci numbers but no luck.
I don't know what else to try.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! I think I found the recursion!
We have 5 - 8 = -3. Take the absolute value of the difference, multiply by 2 to obtain the next term.
8 - 6 = 2, absolute value, multiply by 2 to get 4, etc.
In general, the sequence should be a_n = 2|a_(n-2) - a_(n-1)|. From this, the following term is 16.
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