Page 45 - Ramanujan Yatra

Ramanujan
YATRA
36
The second task required them to guess the number of digits in the 50th Fibonacci number. Their estimates ranged from 4 to 7. As they continued the process of adding pairs of consecutive terms to find the next term, they realised that it would be cumbersome to go on. At this point students were asked to try and generate the Fibonacci sequence on a spreadsheet.
The first step was to create a column of integers from 1 to 50 (by entering 1 in cell A2 followed by the formula =A2+1 in cell A3 and dragging cell A3 till A51 leads to the desired output). In the second step, entering 1 in cells B2 and B3, the formula = B3 + B2 in B4 and double clicking cell B4 generates the Fibonacci sequence as shown in Figure 2. Increasing the column width helps to see that the 50thFibonacci number is 12586269025!
A
B
C
D
Fibonacci Sequence F (n+1)/F(n)
1
1
2
1
1
3
2
2
4
3
1.5
5
5
1.6666667
6
8
1.6
7
13
1.625
8
21
1.6153846
9
34
1.6190476
10
55
1.6176471
11
89
1.6181818
12
144
1.6179775
13
233
1.6180556
14
377
1.6180258
15
610
1.6180371
16
987
1.6180328
17
1597
1.6180344
18
2584
1.6180338
19
4181
1.6180258
20
6765
1.618034
21
10946
1.618034
22
17711
1.618034
23
28667
1.618034
A
B
C
28
317811
1.618034
29
514229
1.618034
30
832040
1.618034
31
1346269
1.618034
32
2178309
1.618034
33
3524578
1.618034
34
5702887
1.618034
35
9227465
1.618034
36
14930352
1.618034
37
241578127
1.618034
38
39088169
1.618034
39
63245986
1.618034
40
102334155
1.618034
41
165580141
1.618034
42
267914296
1.618034
43
433494437
1.618034
44
701408733
1.618034
45
1134903170
1.618034
46
1836311903
1.618034
47
2971215073
1.618034
48
4807526976
1.618034
49
7778742049
1.618034
50
12586269025
1.618034
Figure 2: The first 50 Fibonacci numbers were generated on a spreadsheet