5th Quadratic Sequences Worksheet

Quadratic SequencesLast lesson we learnt how to find an expression for thenth term of a arithmetic (linear) sequence ; one that goes up or down by a constant amount. We foundT= (diff between terms)n+ (zeroth term).So for example the sequence 3, 1, 5, 9..gives the formulaT= 4n+7. We spot arithmeticsequences by looking at the first difference and spotting the , if the seconddifference is constant then you are dealing with aquadratic work out the formula;1. Halve the second difference to get the number ofn2s ( if you had a second differenceof +6 you would have +3n2).2. Write out the original sequence above the terms of your number Subtract then2s from the sequence to give The residue will either be constant or a linear sequence . If it is a linear sequence thenwork out its Finally add the number ofn2s to the formula for the residue and this will be the formulafor the original ExampleFind the formula for the sequence 3,13,27,45,67..Difference table:313274567+10+14+18+22+4+4+4So we have Quadratic sequence with +2n2(half of +4).

Quadratic Sequences Last lesson we learnt how to find an expression for the nth term of a arithmetic (linear) sequence; i.e. one that goes up or down by a constant amount.

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