The sequence of differences is: constant for a linear sequence,

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Presentation transcript:

The sequence of differences is: constant for a linear sequence, The sequence of differences is: constant for a linear sequence, linear for a quadratic sequence, quadratic for a cubic sequence, cubic for a quartic sequence, etc… But it’s exponential for an exponential sequence.

Quadratic Sequence 2n2 + 3n + 1 2n2 3n + 1 4 4 4 9 13 17 21 4 4 4 Quadratic Sequence 9 13 17 21 2n2 + 3n + 1 6 15 28 45 66 2n2 2 8 18 32 50 3n + 1 4 7 10 13 16 Find the sequence of differences Find the sequence of second differences Halve the second difference to find the number in front of the n2. Write out this ?n2 sequence beneath the original one. Work out the differences between these terms and your sequence. Calculate the nth term of this sequence and add it to your ?n2 .