The sequence is too short for a definitive answer.
One possibility is
Un = n2 - 2n + 2 for n = 1, 2, 3, ...
another is
Un = (n3 - n + 6)/6
or
Un = (n3 - 3n2 + 5)/3
There are many more.
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The rule for the sequence is an = xn-1 + xn-2The sequence of numbers, 1, 1, 2, 3, 5, 8, 13, . . . , in which each successive number is equal to the sum of the two preceding numbers.
1, 4, 7, 10, 13, …
x1=0 x2=1 for i > 2, xi= xi-1 + xi-2
1 2 3 4 5 2 5 8 11 14 ... If this is the sequence, the position-to-term rule is 3n-1. However, it could be another sequence depending on the rest of the terms.
The phrase "first difference" is usually associated with a sequence of numbers: a(1), a(2), a(3), a(4), ... . The sequence may have a simple rule for generating the numbers , a complicated rule or, if it is a random sequence, no rule at all.The sequence of first differences is a(2)-a(1), a(3)-a(2), a(4)-a(3), ...