Weve seen that the Fibonacci sequence is defined recursively; each term after the second
Chapter 13, Problem 73(choose chapter or problem)
Weve seen that the Fibonacci sequence is defined recursively; each term after the second is the sum of the previous two terms. There is, in fact, an explicit formula for the nth term of the Fibonacci sequence: This formula was discovered by the French-English mathematician Abraham deMoivre more than 500 years after Fibonacci first introduced the sequence in 1202 in his book Liber Abaci. (For a proof of this formula, see Exercises 74 and 75.) (a) Using algebra (and not your calculator), check that this formula gives the right answers for F1 and F2. (b) Use this formula and your calculator to computer F24 and F25. (c) Use the formula and your calculator to compute F26. Then check your answer by using the results in part (b).
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