Question

Write the following integers as the sum of at least 2 or 3 distinct Fibonacci numbers.a. 19b. 27c. 68d. 97

Answer 1

Given:

Given numbers:

a. 19

b. 27

c. 68

d. 97

To find:

We need to find the Fibonacci numbers whose sum results the above numbers.

Solution:

• The Fibonacci numbers are found by adding the two numbers before it.
• The starting numbers of Fibonacci series are 0 and 1.
• Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584 etc..

Given number are:

1. a. 19

        We need to find the Fibonacci numbers whose sum results in 19.

       Let the numbers are 1, 5, 13.

        $\Rightarrow 1+5+13=19$

        Therefore, the required numbers are 1, 5, 13.

    2. b. 27

        We need to find the Fibonacci numbers whose sum results in 27.

       Let the numbers are 1, 5, 21.

        $\Rightarrow 1+5+21=27$

        Therefore, the required numbers are 1, 5, 21.

     3. c. 68

        We need to find the Fibonacci numbers whose sum results in 68.

       Let the numbers are 13, 55.

        $\Rightarrow 13+55=68$

        Therefore, the required numbers are 13,55.

     4. d. 97

        We need to find the Fibonacci numbers whose sum results in 97.

       Let the numbers are 8, 89.

        $\Rightarrow 8+89=97$

        Therefore, the required numbers are 8, 89.