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. 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. Sample problems are solved and practice problems are provided.We've looked at both arithmetic sequences and geometric sequences let's wrap things up by exploring recursive sequences. These worksheets explain how write the recursive formula for a sequence and find the initial terms of a sequence. When finished with this set of worksheets, students will be able to write the recursive formula for a sequence and find the initial terms of a sequence. Most worksheets contain between eight and ten problems. It also includes ample worksheets for students to practice independently. This set of worksheets contains step-by-step solutions to sample problems, both simple and more complex problems, a review, and a quiz. Space is provided for students to solve each problem. They will find the first four terms of a sequence. Students will write the recursive formula for a given sequence. These are moderately complex problems and a sound understanding of recurrence equations is required in order for students to be successful with these worksheets. In these worksheets, your students will work with recursive sequence. So, it is better that you learn to resolve these sequences because most of the time the recurring equations are more complex. There are countless other series which different researchers use in their hypothesis. to add the previous two numbers to find the next one. In this series, the same formula is used, i.e. One of the most used sequences in the calculations today is the Fibonacci series. All you need to know is the value of term or the terms before the one you are trying to find. In other words, you can solve these sequences by applying the same formula repeatedly. In general terms, recursive sequences or recurring sequences are those sequences which you can solve by using recurring functions. A recursive sequence is a sequence of numbers indexed by an integer and created by solving a recurrence equation.
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