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Geometric Sequences

Geometric Sequences

Geometric Sequences

A sequence can be described as an ordered list of numbers, known as terms. There are many kinds of sequences. Some of them are famous and have even been given names. One example of this is the Fibonacci Sequence. In this chapter a special kind of sequences, called geometric sequences, are presented, defined, and their characteristics are studied.
One characteristic of geometric sequences are that the ratio of any two consecutive terms of the sequence is the same. This is true for any two terms of the sequence. This ratio is referred to as the common ratio. A sequence is geometric if and only if it has a common ratio.
A geometric sequence is completely defined if the common ratio of the sequence, the first term, and the number of terms of the sequence is known. Also it is possible to define a geometric sequence by a rule. These rules can be either recursive or explicit. That a rule is recursive means that to find a specific term in the sequence it is necessary to know its preceding term. If an explicit rule for a sequence is known, any term can be found directly using the rule and the term's number in the sequence.
Geometric sequences and exponential function share similar features. When graphing the terms of an arithmetic sequence they can be shown to fall on the graph of an exponential function.
The content is this chapter is part of Mathleaks' e-Courses. The material is a digital curriculum meeting the common core standards. These e-Courses can be used as a stand-alone curriculum but may also be used as a supplement to other textbooks. In the e-Courses theory is presented using animated instructions, there are problem solving exercises with extensive solutions. The courses also include practice tests, informative videos, and printable worksheets with exercises.

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