Question
Every natural number can be expressed as a sum of Fibonacci numbers, where no number is used more than once. For example, \( 25=21+3+1 \). Express the following number in this way. 155 Finish the sum using only Fibonacci numbers. The natural number can be expressed as \( 155=1+2+3+5+\square \)
Ask by Ingram Peterson. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\(155 = 1 + 2 + 3 + 5 + 144\)
Solution
We start by adding the Fibonacci numbers already given:
\[
1 + 2 + 3 + 5 = 11
\]
Subtract this sum from 155:
\[
155 - 11 = 144
\]
Since 144 is a Fibonacci number (the Fibonacci sequence goes \(1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,\dots\)), we have:
\[
155 = 1 + 2 + 3 + 5 + 144
\]
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Simplify this solution Mind Expander
To express 155 as a sum of Fibonacci numbers, we start with the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, ... Since we've already included 1+2+3+5, we sum these first: 1 + 2 + 3 + 5 = 11. Subtracting from 155, we get 155 - 11 = 144, which is the next Fibonacci number after 89. Therefore, you can complete the expression as: \[ 155 = 1 + 2 + 3 + 5 + 144 \]
