A pattern can
sometimes be seen in a sequence of numbers which leads to a rule
for finding further numbers in the sequence. For example, consider
the sums of odd numbers

1 = 1 = 1^{2}

1 + 3 = 4 = 2^{2}

1 + 3 + 5 = 9 = 3^{2}

1 + 3 + 5 + 7 = 16 = 4^{2}

A Conjecture might be made: the sum of the first n odd numbers is
n^{2}.

The pattern can be illustrated with a Dot Diagram. The diagram
suggests that the pattern continues and can be used to lead
to a general algebraic proof .