Clearly a line of length \(n\) units takes the same time to articulate regardless of how it is composed. Here, we observe that the ratios 50/25010/502/10 are all 1/5. When given a recursive sequence, we can predict and establish their formulas and rules. 2) If the first term is part of a larger series like 3,9,27,81,243,729. A line of length \(n\) contains \(n\) units where each short syllable is one unit and each long syllable is two units. 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. Therefore, we need to subtract 1 from the the month number so it becomes 50+20 (n-1) (Note: 30+20n works as well but is not logical to start off with 30). 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: Substituting the value of r, we get, Therefore, the recursive formula is. The formula to find the recursive formula for the geometric sequence is given by. Now, we shall determine the recursive formula for this geometric sequence. Then he explores equivalent forms the explicit formula and finds the corresponding recursive formula. Also, And, Hence, dividing each term of the sequence, the common ratio is. Problem 73SE: Write an arithmetic sequence. Sal finds an explicit formula of a geometric sequence given the first few terms of the sequences. 11 11 11, 24816 11 11 Select the correct answer below: O Cn -11cn 1, and c, - O Cn - 1, and e 11 Cn 11c,-1, and c C -n 1, and c, 11 O Cn n-1 and c 11. Historically, it is interesting to note that Indian mathematicians were studying these types of numerical sequences well before Fibonacci. Write a recursive formula for a geometric sequence Question Write a recursive formula for the geometric sequence cn given below.
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