converting a recursive sequence to explicit sequence

#CONVERTING A RECURSIVE SEQUENCE TO EXPLICIT SEQUENCE HOW TO#

The roles provide a way for each group member to know they have a contribution to make. Cohen designed group roles to provide equal access to all students during group work. These tasks will be done in small groups of 3-4 people. We will explore sequence in the next few tasks.

#CONVERTING A RECURSIVE SEQUENCE TO EXPLICIT SEQUENCE HOW TO#

Each discipline has preferred ways to work with describing how to calculate each term of a sequence. Mathematicians, biologists, engineers and may others use sequences when modeling real world data. Once you have analyzed the sequences Write a conjecture you think is always true for each of the following: (be sure to write a complete sentence that describes the type of sequence, as well as the value of the difference or ratio)Īn increasing sequence has what kind of value for d?Ī decreasing arithmetic sequence has what kind of value for d?Īn increasing geometric sequence has what kind of value for r?Ī decreasing geometric sequence has what kind of value for r? We will put many examples on the board for analysis. J6 Give examples of each of the following:

For example, ½, ¼, 1/8, …1/2n,… is a geometric sequence with the ratio, r= ½. … is an arithmetic sequence with a difference, d= -2.Ī geometric progression is a sequence of numbers such the ratio of consecutive terms s constant. So each term is easily identified a1 is the first term, a2 is the second term, ai is the ith term of the sequence.Īn arithmetic progression is a sequence of numbers such the difference between consecutive terms is constant. For example, a1, a2 a3, a4,…is a typical way to describe a sequence. A convention is to use subscripts to indicate where in the list a particular object is. This is what we will be exploring in this chapter.Ī sequence is a list of objects with a particular order. So what do we do then? We find an explicit rule to describe any term in the sequence. This recursive rule is not very useful if you don’t need to find the 100th term. This is useful only useful for small values of n. Each term after that is found by adding the previous two terms, that is ai=ai-1+ai-2. Mathematicians are fascinated with the Fibonacci sequence. Second, describe two more places the Fibonacci sequence appears in nature.

Print the image and draw the spirals that represent terms of the Fibonacci sequence and describe how the sequence appears in your image. First find an image of the bottom of a pinecone or a sunflower. J5 Research the Fibonacci sequence for appearances in nature. The size of each chamber follows the Fibonacci Sequence.

Converting a recursive sequence to explicit sequence