A quadratic sequence is given by `U_n=an^2+bn+c`, where `a, b text( and ) c` are constants, `n` is the term and `U_n` is the value of the term. Note that there is no higher power than `n^2` in a quadratic sequence.

The second difference of a quadratic sequence is a constant. Dividing the second difference by 2 gives the coefficient of the `x^2` term.

To work out the quadratic sequence:

work out the first and second differences;

obtain the `a` value by dividing the second difference by 2;

build a sequence using the `an^2` value of each term;

subtract this linear sequence from the original sequence;

work out the `bn + c` from the linear sequence;

add the `an^2` and `bn + c` terms.