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Assuming that the given numbers are the second to fifth numbers of a sequence, any number can be the first (initial) number. It is easy to find a polynomial rule such that the first number is the chosen number, followed by the four numbers that are listed in the question. 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.

For example,

if t(n) = (35n^4 - 282n^3 + 904n^2 - 1125n + 480)/6 then t(1) = 2

if t(n) = (36n^4 - 396n^3 + 975n^2 - 1279n + 600)/6 then t(1) = 6

if t(n) = (37n^4 - 310n^3 + 1046n^2 - 1433n + 720)/6 then t(1) = 10

and so on.

Intermediate values of t(1) are, of course, possible: including fractions. But the coefficients for their rules are more complicated.

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