You may prefer to use T n or some other notation.īack to recurrence relations, any arithmetic progression where the difference between consecutive terms is d, has recurrence relation f(n) = f(n-1 ) + d.Īlthough we only worry here about recurrence relations that involve two terms, it is interesting to note that the Fibonacci sequence has recurrence relation f(n) = f(n-1 ) + f(n-2 ).)įurthermore, with this type of recurrence relations, if we know the recurrence relation of a sequence and we know its first term, then we know the sequence completely. So if f(n) is the value of the n-th term of the pattern/sequence, then f(n) = f(n-1 ) + 1.Īt this point it is worth noting that we will use f(n) for the general term of the sequence here. For instance, in the sequence 4, 5, 6, 7, …, the difference between any two terms is 1. Here we will restrict it to mean the general relation between any pair of terms. So what is a recurrence relation? It is just an equation that links a number of terms of a pattern. For instance, in patterns involving quadratic equations, the recurrence relation involves just a linear relation. This is because the difference pattern is simpler than the original pattern. It seems that it is easier to see the difference(s) between consecutive terms of a pattern than to see the general term. Recurrence relations: Implicitly, recurrence relations are probably the first thing that students use when they are dealing with patterns.
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