Since our recursion uses the two previous terms, our recursive formulas must specify the first two terms. It turns out that each term is the product of the two previous terms. Solution The terms of this sequence are getting large very quickly, which suggests that we may be using either multiplication or exponents. Since our recursion involves two previous terms, we need to specify the value of the first two terms:Įxample 4: Write recursive equations for the sequence 2, 3, 6, 18, 108, 1944, 209952. The syntax of the recursion sequence can be defined as follows- Recursivesequence(expression first-term uppervalue variable). Each term is the sum of the two previous terms. ![]() Solution: This sequence is called the Fibonacci Sequence. A recursive formula designates the starting term, a1, and the nth term of the sequence, an, as an expression containing the previous term (the term before. 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. Complete the recursive formula of the arithmetic sequence 14, 30, 46, 62. 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. Learn how to write recursive formulas in this free math video tutorial by Marios Math Tutoring. 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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