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QUADRATIC RULES
Some problem solving situations involve number sequences which are ruled by a
Quadratic Rule.
You can always identify a pattern as being a quadratic from it's second differences,
which are constant.…read more

Slide 3

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THE SIMPLER RULES
These sequences are nearly always based on n^2 alone. So you do need to
recognise the pattern; 1,4,9,16,25...
The differences between consecutive terms of this pattern are the odd numbers;
3,5,7,9... So, if you find that the differences form an odd numbered sequence,
you know that the pattern is based on n^2…read more

Slide 4

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FIND THE NTH TERM IN THE
SEQUENCE 2,5,10,17,26...
The differences are the odd numbers 3,5,7,9... so we know
that the rule is based on n^2.
The second differences are 2, a constant.
2 5 10 17 26
3 5 7 9 .
2 2 2 etc.
Next, we look for a link with the square numbers. We do this
by subtracting from each term the corresponding square
number.
2 5 10 17 etc.
-1 -4 -9 -16
1 1 1 1
Clearly, the link is +1. So, the nth term is...
n^2+1…read more

Slide 5

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FIND THE NTH TERM IN THE
SEQUENCE 1,6,13,22,33
The differences are 5,7,9,11..so, again, we know that the pattern is n^2.
The second differences are 2, a constant.
Next, we have to find the link. We notice that the first difference is 5 not 3. This
means that the series of square numbers we use start at 4 and NOT 1.
It follows that to obtain 4,9,16,25... from the original sequence simply add 3 to
each term of the sequence.
So, to get from the square numbers to the sequence 1,6,13,22,33... we have to
use (n+1)^2, since the sequence is based on 4,9,16...
The final step in finding the rule is to take away the three, which give the nth
term as:
(n+1)^2-3…read more

Slide 6

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MORE COMPLICATED RULES...…read more

Slide 7

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Comments

daviesg

A good presentation of examples finding the nth term of a non-linear sequence

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