Mathematics, 25.09.2021 14:00 gora2005

The sums of the squares of consecutive Fibonacci numbers beginning with the first Fibonacci number form a pattern when written as a product of two numbers. 12 + 12 = 1 × 2
12 + 12 + 22 = 2 × 3
12 + 12 + 22 + 32 = 3 × 5
12 + 12 + 22 + 32 + 52 =
12 + 12 + 22 + 32 + 52 + 82 =
12 + 12 + 22 + 32 + 52 + 82 + 132 =

a. Compute the three missing sums for the equations shown here. What is the pattern involving the product of two numbers for determining the sum of consecutive Fibonacci numbers?

Answer for a: The product of the last Fibonacci number in the sum times the next Fibonacci
number.

b. Use the pattern from part a to find the sum of the squares of the first 9 Fibonacci numbers.

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The sums of the squares of consecutive Fibonacci numbers beginning with the first Fibonacci number f...