Heuristics to highlight

Look for patterns; Use algebraic equations.

A sequence of numbers u1, u2, u3, u4, ..., is defined by the formula \[{u_n} = {n^5} - 15{n^4} + 85{n^3} - 225{n^2} + 275n - 120\], where n = 1, 2, 3, 4, … Find \[{u_1},{u_2},{u_3},{u_4},{u_5}\] and \[{u_6}\].