What is the number sequence to 1 3 5?

Answer 1

There are infinitely polynomials of order 3 that will give these as the first three numbers and any one of these could be "the" rule. There are also non-polynomial solutions. 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,

t(n) = (-7n^3 + 42n^2 - 65n + 36)/6 gives the sequence 1, 3, 5, 0, ...

t(n) = -1n^3 + 6n^2 - 9n + 5 gives the sequence 1, 3, 5, 1, ...

t(n) = (-1n^3 + 6n^2 - 5n + 3)/3 gives the sequence 1, 3, 5, 5, ...

t(n) = (31n^3 - 186n^2 + 345n - 188)/2 gives the sequence 1, 3, 5, 100, ...

Each one is a valid answer!

The simplest solution, based on a polynomial or order 1 is

t(n) = 2n - 1 for n = 1, 2, 3