Question

Fibonacci numbers – for loops

We’ll define the Fibonacci numbers to be an integer sequence starting with 1, 1, and where each subsequent element is got by adding the previous two elements:

1, 1, 2, 3, 5, 8, . . .

(Mathematicians start with 0, 1, . . . , but we want to avoid zeros because you can’t take their log. )

Write a python programme in a Jupyter notebook which uses a for-loop to fill an array with the first 20 Fibonacci numbers. You will need to initialise the first two elements of the array before you enter the loop. Your programme should then list the Fibonacci numbers.

Finally plot a semi-log graph of the numbers versus their place in the sequence.

Answer 1

Program in python:

#importing module for creating array
import array as arr
#importing module for creating plot
import matplotlib.pyplot as pt

# create array with int type
ar = arr.array('i', [1, 1])
#inserting n more values to the array
n=20
for i in range (1, n):
    ar.insert((i+1),ar[i]+ar[i-1])

#creating list to store the index position
ls=[]
print ("Array element are: ", end =" ")
for i in range (0, len(ar)):
    #printing the array element
    print (ar[i], end =" ")
    #adding index to the list
    ls.append(i)
#calling function to plot the graph using function
pt.semilogx(ls, ar)
#labelling the x and y axis
pt.xlabel("Index")
pt.ylabel("Value")
#showing the graph to the user
pt.show()

Indentation:

Output: