The Fibonacci sequence starts as: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. To express 160 as a sum of non-consecutive Fibonacci numbers, we can use Zeckendorf's Theorem, which states that every positive integer can be uniquely represented as a sum of non-consecutive Fibonacci numbers.

Let's break down 160 using the Fibonacci sequence:

• The largest Fibonacci number less than or equal to 160 is 144.

• Subtracting 144 from 160 gives:
  $160 - 144 = 16$

• The largest Fibonacci number less than or equal to 16 is 13.

• Subtracting 13 from 16 gives:
  $16 - 13 = 3$

• The largest Fibonacci number less than or equal to 3 is 3.

Thus, the sum is: $160 = 144 + 13 + 3$

Since 144, 13, and 3 are non-consecutive Fibonacci numbers, this is the desired representation.

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Do you want more details on this solution or have any further questions? Here are 5 related questions to expand on this:

1. What is Zeckendorf's Theorem in detail?
2. How can you find Fibonacci numbers efficiently for larger sums?
3. Can any integer be written as a sum of non-consecutive Fibonacci numbers?
4. What is the general formula for Fibonacci numbers?
5. How do Fibonacci numbers relate to the golden ratio?

Tip: Always check that no two Fibonacci numbers in your sum are consecutive to ensure correctness according to Zeckendorf’s theorem!