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Carom Maths
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Zeroes of a Recurrence Relation
Carom Maths provides this resource for teachers and students of A Level mathematics.
The Fibonacci sequence is an example of a linear recurrence relation (LRS). A matrix is used to calculate future terms, as well as running the sequence backwards to see how many zeroes appear. Algebra is used to prove the maximum number of zeroes it is possible to find in an order-2 LRS before students use a matrix to locate the position of zeroes in an order-3 linear recurrence relation.
The activity is designed to explore aspects of the subject which may not normally be encountered, to encourage new ways to approach a problem mathematically and to broaden the range of tools that an A Level mathematician can call upon if necessary.
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