Thu Jun 12, 2014 5:29 pm by gm 


Hello! I have been struggling to solve this number sequence puzzle for a while now and I have been unsuccessful so far. I would like to see how you do. If you have an answer, please post how you got to that answer.
Here is the sequence:
4, 8, 16, 26, 41, 57, 79, 104, 138, 184, 241, ? 




Fri Sep 23, 2016 2:47 pm by schizomidget 


difference between each terms of the sequence is 4, 8, 10, 15, 16, 22, 34, 46, and 57, respectively. Now let's make that our new sequence.
Then the difference between each terms of the new sequence is 4, 2, 5, 1, 6, 12, 12, and 11. Let''s make this our new sequence this time.
311.
The differences between each term of the new sequence is 2, 3, 4, 5, 6, 0, and then 1. You see the pattern? (increasing by 1 with alternating signs, and when it reaches 6, it starts from 0 again)
Using inductive reasoning, we can infer that the next term will be... 2, 3, 4, 5, 6, 0, 1, and 2...so 2 will be the next term of the newest sequence.
And if the last term is 2, then that means the last term of the 3rd sequence will be 11+2=13.
And if this last term is 13, then that means the last term of the 2nd sequence will be 57+13=70.
And if this last term is 70, then that means the last term of the original sequence will be 241+70=311. 






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