!Fibonacci SequencesVideo 287a on www.corbettmaths.com Question 1: The =irst 4 numbers in the Fibonacci sequence are (a) What is the 5th term of the Fibonacci sequence?(b) What is the 6th term of the Fibonacci sequence?(c) Describe the rule for continuing the Fibonacci sequence.Question 2: Find the next three terms of the following Fibonacci-style sequences(a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) Question 3: Find the missing term in each of the Fibonacci-style sequences below.(a) (b) (c) (d) (e) (f) (g) (h) (i) Question 1: For each of the following Fibonacci-style sequences, =ind the next 4 terms.(a) (b) (c) (d) (e) (f) ExamplesWorkout1, 1, 2, 3, . . .2, 4, 6, 10, . . . 3, 6, 9, 15, . . . 4, 8, 12, 20, . . .15, 23, 38, 62, . . . 5, 12, 17, 29, . . . −3, 5, 2, 7, . . .35, 60, 95, 155, . . . −1, − 3, − 4, − 7, . . . 1.2, 2.7, 3.9, 6.6, . . .0.11, 2.32, 2.43, 4.75, . . . −5.1, 1.1, − 4, − 2.9, . . . −0.5, − 0.7, − 1.2, − 1.9, . . .111 , 311 , 411 , 711 , . . . 56 , 1112 , 74 , 83 , . . . − 15 , 12 , 310 , 45 , . . .□ , 13, 20, 33, . . . 11, □ , 26, 41, . . . □ , 69, 109, 178, . . .□ , 3.7, 4.9, 8.6, . . . 26.3, □ , 64.4, 102.5, . . . 10.25, □ , 25.75, 41.25, . . .6, □ , 4, 2, . . . − 12, □ , − 4, 4, . . . □ , − 54 , − 2, − 134 . . .Applya, 4a, 5a, 9a, . . . 3x, 3x + y, 6x + y, 9x + 2y, . . .6a, − 2a, 4a, 2a, . . . 2y, y + z, 3y + z, . . .4x − 5y, 2x − y, 6x − 6y, . . . −x, x + y, y, . . .© CORBETTMATHS 2019Click hereiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiifhfliTooartpifsssaia.ee !Fibonacci SequencesVideo 287a on www.corbettmaths.comQuestion 2: Beth wants to generate a Fibonacci style sequence.The =irst term is 3 and the second term is 4.(a) Find the 3rd term.(b) Find the 4th term.Beth thinks that the sum of the =irst ten terms is equal to 11 times the 7th termof her sequence.(c) Show that Beth is correct.Question 3: Using the =irst term of and the second term of , prove your answer toQuestion 2 (c).Question 4: Ethan generates the pattern below(a) Draw Pattern 6(b) What is the length of each side of square F?(c) What is the length of each side of square G?(d) What is the length of each side of square H?(e) What do you notice about your answers to (b), (c) and (d)?Question 5: Dylan is researching what happens when a termin the Fibonacci sequence is divided by the term before it.(a) Find the missing answers(b) What do you notice?(c) Research the Golden Number. x yAnswers© CORBETTMATHS 2019Click hereiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii Textbook 287aAnswers1a) 5 b) 8 c) “to get the next term, add the previous 2”2a) 16, 26, 42 b) 24, 39, 63 c) 32, 52, 84d) 99, 160, 259 e) 46, 75, 121 f) 9, 16, 25g) 250, 405, 655 h) -11, -18, -29 i) 10.5, 17.1, 27.6j) 7.18, 11.93, 19.11 k) -6.9, -9.8, -16.7 l) -3.1, -5, -8.1m) 1, 1 7/11, 2 7/11 n) 53/12, 85/12, 23/2 o) 11/10, 19/10, 33a) 7 b) 15 c) 40d) 1.2 e) 38.1 f) 15.5g) -1.8 h) 7.6 i) -0.75Apply1a) 14a, 23a, 37a, 60a b) 15x + 3y, 24x + 5y, 39x + 8y, 63x + 13yc) 6a, 8a, 14a, 22a d) 4y + 2z, 7y + 3z, 11y + 5z, 18y + 8ze) 8x – 7y, 14x – 13y, 22x – 20y, 36x – 33y f) x + 2y, x + 3y, 2x + 5y, 3x + 8y2a) 7 b) 11c) Sequence is 3, 4, 7, 11, 18, 29, 47, 76, 123, 199…Sum of these first ten terms is 517The seventh term is 47.47 x 11 = 517, showing that Beth is correct 3) 1st Term: x2nd Term: y3rd Term: x + y4th Term: x + y + y = x + 2yThe sequence continues: 2x + 3y, 3x + 5y, 5x + 8y, 8x + 13y, 13x + 21y, 21x + 34ySum of the first 10 terms = 55x + 88y11 times the 7th term = 11(5x + 8y) = 55x + 88y4)F b) 8c) 13d) 21e) They are all part of the Fibonacci sequence, starting 1, 1, 2, 3,…..5a) 8 ÷ 5 = 1.6 13 ÷ 8 = 1.626 21 ÷ 13 =1.6153….b) Each term is around 1.6, and the sequence appears to be convergingThe limit of this sequence is the “Golden Number” or “Golden Ratio”, usually called φ (“phi”)
