Recurance Relations
Recurance Relations |
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MathsDirect |
| A sequence is sometimes defined by a
recurrence relation. This tells you how to find the next term,
given the current term. For example: |
| This tells you that the first term is 2. To find the next term you add 2 |
| This gives the sequence |
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| A second example |
| To generate each term, you double the previous term, then add 1. |
| This gives |
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| The rule could refer to more than one of the previous terms, such as |
| This says that to generate each term, you add the previous 2 terms together. Obviously you need to be given 2 starting terms. |
| This gives the famous Fibonacce series |
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| A recurrence relation can give a convergent sequence |
| Each term is half the previous term. |
| This gives |
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| A recurrence relation can also give an oscillating sequence. |
| To generate each term, subtract the previous term from 1. |
| This gives |
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