Concept explainers
Fibonacci Properties The Fibonacci sequence has many unusual properties. Experiment to decide which of the following properties are valid. Note:
a.
b.
c.
d.
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Chapter 1 Solutions
Mathematical Excursions (MindTap Course List)
- Fibonaccis RabbitsFibonacci posed the following problem: Suppose that rabbits live forever and that every month each pair produces a new pair that becomes productive at age 2 months. If we start with one newborn pair, how many pairs of rabbits will we have in the n th month? Show that the answer if Fn, where Fn is the n th term of the Fibonacci sequence.arrow_forwardSequences of Powers the following sequence of perfect squares is not arithmetic. 1, 4, 9, 16, 25, 36, 49, 64, 81, . . . The related sequence formed from the first differences of this sequence, however, is arithmetic. (a) Write the first eight terms of the related arithmetic sequence described above. What is the nth term of this sequence? (b) Explain how to find an arithmetic sequence that is related to the following sequence of perfect cubes. 1, 8, 27, 64, 125, 216, 343, 512, 729, . . . (c) Write the first seven terms of the related arithmetic sequence in part (b) and find the nth term of the sequence. (d) Explain how to find an arithmetic sequence that is related to the following sequence of perfect fourth powers. 1, 16, 81, 256, 625, 1296, 2401, 4096, 6561, . . . (e) Write the first six terms of the related arithmetic sequence in part (d) and find the nth term of the sequence.arrow_forwardSum of a Finite Arithmetic Sequence Find the sum of the integers from 30 to 80.arrow_forward
- Musical Frequencies The frequencies of musical notes (measured in cycles per second) from a geometric sequence. Middle C has a frequency of 256, and the C that is an octave higher has a frequency of 512. Find the frequency of C two octaves below middle C.arrow_forwardPrize Money A county fair is holding a baked goods competition in which the top eight bakers receive cash prizes. First place receives $200, second place receives $175, third place receives $150, and so on. (a) Write the nth term (an) of a sequence that represents the cash prize received in terms of the place n the baked good is awarded. (b) Find the total amount of prize money awarded at the competition.arrow_forward
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