Question

What should come in the place of question mark in the following series - 1, 4, 13, 30, 59, ?

Answer 1

1
2^2 + 1^3 - 1= 4
3^2 + 2^3 - 4= 13
4^2 + 3^3 - 13 = 30
5^2 + 4^3 - 30 = 59
6^2 + 5^3 - 59 = 102.

Comments

Complex one :)

Answer 2

1. the answer will be -104

Comments

What is the logic?

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It's Incorrect.

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What was your logic ? Please explain.

Answer 3

I got 106; it goes up by +3, +9, +17, +29, etc. Those numbers were thought to have an incremental addition too, so basically 3+b=9, 9+x=17, etc. with b=6 and x=8. There were incremental differences there too, because 1*2=2 between the 6 and 8, 2*2=4 between the 8 and 12, so the next pattern could be 2*3=6 between 12 and the increment, so adding 6 to 12 would be 18. Add 18 to the +29, then you have +47. Add 47 to 59 and you would get 106.

Comments

To call something a pattern we must have atleast three data points verified ( in your explanation 2*1, 2*2 ... etc., ).
If you had another number to check your theory you could have done it. But since I didn't give you another number to check this and the fact that you had only 2 data points backing up your theory should have been enough to confirm that the theory could be very easily wrong.

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Can I ask why specifically 3 data points are needed to back up the pattern (like why not at least 4, 5, etc.)

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For instance a simple series like
1,2 can be assumed to have its next term as 1,2,4 (doubles every step) or 1,2,3 (simple incremental series) or 1,2,1 (repeating 1 and 2 series) or 1,2,5 (differences are increasing by 2 starting from 1 then 3 and so on ) etc.,
So atleast 3 or more data points are needed to predict the behavior of a series, or else we could be easily wrong.