Clearly a line of length \(n\) units takes the same time to articulate regardless of how it is composed. A line of length \(n\) contains \(n\) units where each short syllable is one unit and each long syllable is two units. Suppose also that each long syllable takes twice as long to articulate as a short syllable. Suppose we assume that lines are composed of syllables which are either short or long. ![]() In particular, about fifty years before Fibonacci introduced his sequence, Acharya Hemachandra (1089 – 1173) considered the following problem, which is from the biography of Hemachandra in the MacTutor History of Mathematics Archive: Then each term is nine times the previous term. For example, suppose the common ratio is 9. Each term is the product of the common ratio and the previous term. A recursive formula allows us to find any term of a geometric sequence by using the previous term. ![]() Historically, it is interesting to note that Indian mathematicians were studying these types of numerical sequences well before Fibonacci. Using Recursive Formulas for Geometric Sequences. We can express the rule as a function of a n 1. They are easy to turn into videos or interactive with google slides.\). A pattern or an equation in terms of a n 1 or even a n 2 that applies throughout the sequence. These notes are great for in class or distance learning! They include clear instruction, key words & vocabulary, and a variety of examples. You can find a video where I work out these notes on my YouTube channel here. Recursive formula is ana(n-1)xx1/5 In a Geometric sequence, the ratio of each term to its preceding term is always constant and is known as common ratio r.
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