Subjects algebra

Fibonacci Sequence 550Afc

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1. The problem is to understand the Fibonacci sequence and find its terms. 2. The Fibonacci sequence is defined by the recurrence relation: $$F_n = F_{n-1} + F_{n-2}$$ with initial terms: $$F_0 = 0, \quad F_1 = 1$$ 3. This means each term is the sum of the two preceding terms. 4. Let's calculate the first few terms: $$F_0 = 0$$ $$F_1 = 1$$ $$F_2 = F_1 + F_0 = 1 + 0 = 1$$ $$F_3 = F_2 + F_1 = 1 + 1 = 2$$ $$F_4 = F_3 + F_2 = 2 + 1 = 3$$ $$F_5 = F_4 + F_3 = 3 + 2 = 5$$ 5. So the sequence starts as: 0, 1, 1, 2, 3, 5, ... 6. This sequence appears in many natural phenomena and has interesting mathematical properties.