The
Fibonacci sequence is a well-known , where the first two are both
1. Subsequent terms in the sequence are generated by adding the two preceding numbers.
Starting from the third term onward, the sequence can be represented using a rule.
a1=1a2=1an=an−1+an−2
This is an example of as the
nth term depends on the values of the previous two terms. This indicates that to find, for instance, the seventh term
a7 of the sequence, it is necessary to have information about the fifth and sixth terms.
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an=an−1+an−2
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n=7
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a7=a6+a5
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a6=8 and a5=5
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a7=8+5
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Evaluate
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a7=13
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The sequence is named after the Italian mathematician Leonardo Fibonacci, who used it to describe how pairs of rabbits increases as they multiply under certain conditions. Sometimes, the first two numbers are defined as a1=0 and a2=1. This, however, does not change the sequence in any way other than by increasing the index of every term by one compared to the previously mentioned definition.