7. Ratio and Fibonacci


PROJECT 7.6 n = 1


Block Sequences 2 n = 2


n = 3


(i) Draw the next two stages (ii) Write the number of white tiles for the first 6 stages as a sequence (iii) How many white tiles are there in stage 10 and in stage 50? Can you give a general expression for the number of white tiles in any stage (iv) Try to explain why (n + 1)2


– 1; n2 + 2n; n(n + 2) would all work as the general expression for the number of tiles in stage n.


PROJECT 7.7 n = 1


Block Sequences 3 n = 2


n = 3


(i) Draw the next two stages (ii) Write the number of white tiles for the first 6 stages as a sequence (iii) How many white tiles are there in stage 10 and in stage 50? Can you give a general expression for the number of white tiles in any stage (iv) What stage will have 101 white tiles?


Ratio:


To divide numbers in a certain ratio: Example 3:


Anna gets , Eamon gets €70,


7 1


10 100 ×=


7 10


10 100 ×=


3


Divide €100 between Anna and Eamon in the ratio of 7 : 3 Add 7 + 3 = 10


3 10 €30


75


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