Project 2: Number Patterns, p. 9 7. Find the pattern when the squares of the Fibonacci numbers are added: a. Complete the table for the first six rows: The squares of Fibonacci Numbers Pattern Sum (F1)2 (F1)2 + (F2)² = 12 = 12 + 12 = 1 x1 = 1 x 2 1 1+1 2 (F1)2 + (F2)² + (F3)² = 1² + 1²2 + 22 = 1+1+4 6 = 2 x ? %D %3D %3D =_x %3D | d h bact he en fro the larger reault =_X- %3D - the ailt t equal lo the Lars allest and largest-look at %3D %3D the soquence61,1.2,3 vere the anerer of 3. What can y Complete the blanks and the next three rows. Hint: look for two special numbers that multiply to get the sum. b. Explain the pattern of the answers in words. Hint: relate the two multiplied numbers to the numbers you just added. and then uotrect the emaller FHE era lkel 3nd &nd d largest in werds the rtult ie bo c. Use the pattern to predict the sum when 12 + 1² + 22 + 32 + 52 + ... + 2332 is added. Your answer should show that you know how to get the answer using the pattern, without having to actually add up all the numbers! Hint: which subscript does 233 have? Which subscript will the two numbers in your answer have? How do you know? II IL | II II