Mathematicians have used sequences of numbers to calculate and to describe things found in nature. 1. List the first 15

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Mathematicians Have Used Sequences Of Numbers To Calculate And To Describe Things Found In Nature 1 List The First 15 1 (265.52 KiB) Viewed 84 times

Mathematicians have used sequences of numbers to calculate and to describe things found in nature. 1. List the first 15 terms of the Fibonacci sequence and describe three examples of where it can be found in nature. 2. What is the relationship between Fibonacci numbers and the Golden Ratio? What symbol is given to the Golden Ratio? 3. Find the 25th triangular number (use a rule). Use Excel to produce the first 25 triangular numbers. Copy the table into your report and show the formula you typed into Excel 4. One way to add up n natural numbers can be described as: ( 3 ) which is in combinations' form. Use this rule to find the sum of the first 20 natural numbers (show your working). 5. Explain how Gauss might have added up the first 20 numbers. 6. Write out the first 10 terms in the Lazy Caterer's sequence, showing how you worked them out. Use Excel to produce the first 20 numbers. Copy the table into your report and show the formula you typed into Excel. What are the minimum and maximum number of pieces that could be produced by 10 cuts? 7. In the Look and Say sequence, write the numbers that come before and after 31131211131221. 8. Describe and analyse the diagram below. You could include description of how to construct it, a table of values containing information such as the size of the angle at the centre, the length of the sides. You should include some other information, calculation, pattern, or statement about the diagram 2 V3 VZ 1 V6 7