To determine which of the given sets of numbers follows the Fibonacci sequence concept, let's first review how the Fibonacci sequence works:

• The Fibonacci sequence starts with two numbers: 0 and 1 (or sometimes 1 and 1).
• Each subsequent number is the sum of the two preceding ones:
  $F(n) = F(n-1) + F(n-2)$

Let's analyze the sets:

1. Set 1: 1, 2, 3, 4, 5, 6

   • The difference between consecutive numbers is constant (+1).
   • This is an arithmetic sequence, not a Fibonacci sequence.

2. Set 2: 3, 6, 9, 12, 15, 18

   • The difference between consecutive numbers is constant (+3).
   • This is another arithmetic sequence, not a Fibonacci sequence.

3. Set 3: 2, 4, 6, 10, 16, 26

   • Let's check the sum of the two previous numbers for the Fibonacci pattern:
     • 2 + 4 = 6 (Correct)
     • 4 + 6 = 10 (Correct)
     • 6 + 10 = 16 (Correct)
     • 10 + 16 = 26 (Correct)
   • This set follows the Fibonacci sequence.

4. Set 4: 4, 2, 1, 1/2, 1/4, 1/8

   • The numbers are halving each time, but it's not following the sum rule of the Fibonacci sequence.
   • This is a geometric sequence, not a Fibonacci sequence.

Conclusion:

The set 2, 4, 6, 10, 16, 26 follows the concept of the Fibonacci sequence.

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Would you like a detailed explanation of Fibonacci sequences or have any questions? Here are some related topics to explore:

1. How to generate a Fibonacci sequence programmatically.
2. The relationship between Fibonacci numbers and the golden ratio.
3. How to extend the Fibonacci sequence into negative numbers (the negafibonacci sequence).
4. The connection between Fibonacci numbers and nature.
5. The differences between arithmetic, geometric, and Fibonacci sequences.

Tip: Fibonacci numbers often appear in nature, such as in the arrangement of leaves, the branching of trees, or the spiral of shells!