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Date: 13th October 2008
Maths Notes Quadratic Sequences
When we get a sequence that doesn't go up/down in the same numbers, then the
sequence is not linear.
Quadratic sequences are sequences that have a constant second difference.
The first difference is not the same, therefore it is not a linear sequence.
We then work out the second difference: the difference of the first difference, and this
proves to be the same (constant).
When the second difference is constant, it means that the equation will contain an n2 term.
The n2 sequence will always be the same. When the sequence doesn't have an n2 in it,
then the n2 sequence would just change to the appropriate sequence, eg. 2n2 sequence.
The difference between the sequence numbers to the n2 sequence numbers is 3 all the
time. Therefore it is 3 more than the n2 term.
So the equation is: n2 + 3 (test on any number in the sequence to check if this works)
The second difference tells us how many n2s there are. The rule is to halve the second
If the difference was 2, it would be n2 if the difference was 4, it would be 2n2 and so on...