Each term is the sum of the two previous terms. Solution: This sequence is called the Fibonacci Sequence. Solution: The first term is 2, and each term after that is twice the previous term, so the equations are:Įxample 3: Write recursive equations for the sequence 1, 1, 2, 3, 5, 8, 13. Notice that we had to specify n > 1, because if n = 1, there is no previous term!Įxample 2: Write recursive equations for the sequence 2, 4, 8, 16. Solution: The first term of the sequence is 5, and each term is 2 more than the previous term, so our equations are: Recursive equations usually come in pairs: the first equation tells us what the first term is, and the second equation tells us how to get the n th term in relation to the previous term (or terms).Įxample 1: Write recursive equations for the sequence 5, 7, 9, 11. If a sequence is recursive, we can write recursive equations for the sequence. In a geometric sequence, each term is obtained by multiplying the previous term by a specific number. Why? In an arithmetic sequence, each term is obtained by adding a specific number to the previous term. If we go with that definition of a recursive sequence, then both arithmetic sequences and geometric sequences are also recursive. Recursion is the process of starting with an element and performing a specific process to obtain the next term. We've looked at both arithmetic sequences and geometric sequences let's wrap things up by exploring recursive sequences.
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