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• Created by: Kelly:)
• Created on: 30-05-11 16:05

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Finding the nth term of these sequences can be a little more difficult
than soling the linear sequences.
Find the nth term to this sequence:
8 19 36 59 88 123
11 17 23 29 35
6
6 6 6
First you find the first difference between them.
Secondly, you find the second difference between the first
differences, these will all be equal.
Thirdly, you need to halve the second difference to find the
coefficient of n^2, so in this case it's: 3n^2.
Write out the original sequence again and underneath write out the
sequence for 3n^2:
8 19 36 59 88 123
3 12 27 48 75 108
We then need to observe the differences between these two
sequences and work out the rest of our nth equation.
Differences:
5 7 9 11 13 15

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As we know from solving linear sequences the difference between
these numbers determines the number we multiply `n' by, so in this
case its 2n.
So far we have: 3n^2 + 2n
Looking back over our sequences once more shows us that we need
to + 3 to all of our numbers to get back to the original sequence.
Now have a go yourself.
Find the nth term of these