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There are infinitely many possible answers because there are infinitely many polynomials of order 6 (or higher) that will give these as the first six numbers and any one of these could be "the" rule. Short of reading the mind of the person who posed the question, there is no way of determining which of the infinitely many solutions is the "correct" one.
The simplest solution, however, is possibly the following:
U(n) = x^2 + 3*x - 2 for n = 1 ,2, 3, ...
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What is the nth term for the sequence 2 8 16 26 38?
2 + ((6 + 2 * (n - 1) * (n - 1))
What is the nth term of 14 20 26 32 38?
[ 6n + 8 ] is.
What is the nth term for 8 16 26 38 52?
Each number is increasing by increments of 8 10 12 14 ... etc and so the next number will be 52+16 = 68
What is the nth term of 2 8 16 26 38?
It depends what the next number in the sequence is. The simplest polynomial for those 5 terms is: U{n} = n² + 3n - 2
What is the nth term for 6 11 18 27 38?
The nth term of the sequence is (n + 1)2 + 2.
