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Consider the Fibonacci sequence 1,1,2,3,5,8,13,21,34,55,89,…. . The first two numbers are 1 and 1. When you...

Consider the Fibonacci sequence 1,1,2,3,5,8,13,21,34,55,89,…. . The first two numbers are 1 and 1. When you add these numbers you get 2 = 1+1, which becomes the third number in the sequence. When you add the second and third numbers, you get 3 = 1+2, which becomes the fourth number in the sequence. When you add the third and fourth numbers, you get 5 = 2+3, which becomes the fifth number in the sequence; and so on to generate the sequence. Write a short Excel program that generates the first 50 numbers of the Fibonacci sequence, using 1 and 1 as the first two numbers to start the sequence. Put these numbers in Column A in Excel. Also, in the next column in Excel (Column B), divide each number in the sequence by the previous number in the sequence. This column is a new sequence of numbers. Start Column B in Row 2. To what number does the sequence of the quotients in Column B converge? Use the 2-D Bar Chart tool in Excel to graph the first 10 ratios in Column B

Expert Solution

The excel images with correct steps are shown below.

Step 1: The first and second rows in column are filled with the value '1'.

Step 2: In the third row, the formula '' is applied (enter key is pressed).

Step 3: The third row/cell mentioned above is copeid (ctrl+c) and then the cells from 4th to 50th rows are selected, and then paste option is enforced (by ctrl+v), thereby providing us the first column.

Step 4: Cell in 2nd row and column B is selected, and formula '' is applied.

Step 5: By analogous procedure, the column B is created by copying its second row and pasting the formula until all the values in column are covered.

We now have the two two columns. The values may seem that they exactly (not according to charts, but to the numbers in sight) converges from (25-1) 24th term of of the second column, as can be seen in the image below, but the convergence actually starts from the 7th term in column B. It is after the 7th term there that the values lose their volatile (ie increasing and then decreasing and then again increasing, and so on) trend.

The bar chart is as below, which is created by selecting first 10 cells in column B, and then goind to Insert option, then chart, and then choosing Bar Chart in the option there.

milcah answered 1 year ago

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