A python program for summation of any number range

Arithmetic Progression through Python

What is Arithmetic progression?

A sequence a₁ , a₂ , a₃ ,…, a_n ,… is called arithmetic sequence or arithmetic progression if a_{n + 1} = a_n + d, n ∈ N, where a₁ is called the first term and the constant term d is called the common difference of the A.P.

Let us consider an A.P. (in its standard form) with first term a and common difference d, i.e., a, a + d, a + 2d, ... 

Then the n th term (general term) of the A.P. is an = a + (n – 1) d. 

We can verify the following simple properties of an A.P. : 

(i) If a constant is added to each term of an A.P., the resulting sequence is also an A.P. 

(ii) If a constant is subtracted from each term of an A.P., the resulting sequence is also an A.P.

 

(iii) If each term of an A.P. is multiplied by a constant, then the resulting sequence is also an A.P. 

(iv) If each term of an A.P. is divided by a non-zero constant then the resulting sequence is also an A.P. Here, we shall use the following notations for an arithmetic progression: a = the first term, l = the last term, d = common difference, n = the number of terms. Sn = the sum to n terms of A.P. Let a, a + d, a + 2d, …, a + (n – 1) d be an A.P. Then l = a + (n – 1) d

Let's understand AP in simple example ,

 1+2+3+4+ .... +50 (Sum of sequence Natural number )  

or

 0+2+4+6+ .... +48 (Sum of sequence of Even number)

or

1+3+5+7 +.....+49 (sum of sequence of Odd number )

If you look at above three sequences , 

• First sequence is sum of natural number . between 1 and 2 ,  2 and 3 etc, there difference is 1 .
• Second sequence is sum of even number . There common difference is 2 . 
• In third sequence , the common difference between the number is also 2 .

A.P. can be done mathematical formula , but it can also be done through coding  . In this blog we will discuss how to add sequence of numbers through python . 

Algorithm : 

• If You want to calculate sum of a to b range , your input will be a b c  you get following answers :

0+1+2+3+4+5+6+.......+50  =Result (Whole number summation)

                and

0+2+4+6+8+10+.....+50 = Result (Even number summation)

               and 

1+3+5+7+9+11+....+49 = Result (Odd number summation)

Where a= starting point (for above case, a=0) , b = Stopping point( for above case ,b=50) and for c = step size(if step size is 2 , this program will take 0,2,4,6,.....,50)(for above case c=0)

If  c not equal to zero , it only print the summation of specific number range with specific step .

Source code :

 a=0  
 a1=0  
 x,y,z = [int(f) for f in input("Enter the number range to do summation (START STOP STEP):").split()]  
 if z==0 :  
    for i in range(x,y+1):  
      if (i % 2 ==0):  
        a += i  
      else:  
        a1 += i  
    print(f"Sum of even number between {x} to {y} range :",a)  
    print(f"Sum of odd number between {x} to {y} range :",a1)  
    print(f"Sum of whole number between {x} to {y} range :",a1+a)  
 else :  
    for i in range(x,y+1,z):  
      a += i  
    print(f"Sum of the numbers between {x} to {y} range with step {z} :",a)  

Output:

 >>>Enter the number range to do summation (START STOP STEP):0 50 2  
 >>>Sum of the numbers between 0 to 50 range with step 2 : 650  

                                                                       Another 

 >>>Enter the number range to do summation (START STOP STEP):0 50 0  
 >>>Sum of even number between 0 to 50 range : 650  
    Sum of odd number between 0 to 50 range : 625  
    Sum of whole number between 0 to 50 range : 1275