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1,1,2,3,5,8,13,21,34

2025-05-04 #13 #21 #34 阅读量：3

The given sequence is the Fibonacci sequence, where each number is the sum of the two preceding ones, starting from 1 and 1. Here's the breakdown:

1,1,2,3,5,8,13,21,34

  • Pattern:

    • ( F(n) = F(n-1) + F(n-2) ), with ( F(1) = 1 ) and ( F(2) = 1 ).

  • Sequence:

    • ( 1, 1, 2, 3, 5, 8, 13, 21, 34, dots )

  • Next Terms:

    • After 34, the sequence continues as ( 55, 89, 144, dots ).

  • Key Properties:
  • The ratio of consecutive terms approaches the golden ratio (( phi approx 1.618 )). For example, ( frac{34}{21} approx 1.619 ).
  • Appears in nature (e.g., branching trees, flower petals) and mathematics (e.g., number theory, combinatorics).

    • This sequence is foundational in mathematics and has widespread applications in science, art, and computer algorithms.