Stage: 4 Challenge Level: 
The $n$th term of a sequence is given by the formula
$n^3 + 11n$.
Find the first four terms of the sequence given by this formula and the first term of the sequence which is bigger than one million. Prove that all terms of the sequence are divisible by $6$.
Factorisation (algebraic). Inequality/inequalities. Factors and multiples. Visualising. Manipulating algebraic expressions/formulae. Mathematical reasoning & proof. Number theory. Algebra - generally. Sequences. Divisibility.
Published December 2001,January 2002.
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