Wear a helmet. Even when coding.

exercises > sum-of-first-n

Exercise #17: Sum of First N Numbers
by Zoran Horvat @zoranh75

Problem Statement

Given a positive number N, write a function which returns sum of numbers 1 + 2 + ... + N.

Example: If N is 5, then return value should be 15 (1 + 2 + 3 + 4 + 5 = 15).

Problem Analysis

This task can be solved quickly by iterating through the sequence:

function Sum(n)
    sum = 0
    for i = 1 to n
        sum = sum + i
    return sum

This function runs in time O(N) and space O(1). Now we can ask if there is a better solution in terms of running time. In order to make the function run in constant time, we need to entail a definite form of the sum. This is easy to do and here is one possible way:

The function which calculates the sum of the sequence in O(1) time and O(1) space is then:
function Sum(n)
    return n * (n + 1) / 2


Below is the console application in C# which lets the user enter N and then prints the sum of the sequence of N elements.

using System;

namespace SumOfSequence

    public class Program

        static int Sum(int n)
            return n * (n + 1)  2;

        static void Main(string[] args)

            while (true)

                Console.Write("Enter sequence length (zero to exit): ");
                int n = int.Parse(Console.ReadLine());

                if (n <= 0)

                Console.WriteLine("Sum of the sequence is {0}\n", Sum(n));





Here is the possible output of the application listed above:

Enter sequence length (zero to exit): 4
Sum of the sequence is 10

Enter sequence length (zero to exit): 5
Sum of the sequence is 15

Enter sequence length (zero to exit): 43127
Sum of the sequence is 929990628

Enter sequence length (zero to exit): 0

See also:

Published: Dec 14, 2013


Zoran is software architect dedicated to clean design and CTO in a growing software company. Since 2014 Zoran is an author at Pluralsight where he is preparing a series of courses on design patterns, writing unit and integration tests and applying methods to improve code design and long-term maintainability.

Follow him on Twitter @zoranh75 to receive updates and links to new articles.

Watch Zoran's video courses at (requires registration):

Tactical Design Patterns in .NET: Managing Responsibilities

Applying a design pattern to a real-world problem is not as straightforward as literature implicitly tells us. It is a more engaged process. This course gives an insight into tactical decisions we need to make when applying design patterns that have to do with separating and implementing class responsibilities. More...

Tactical Design Patterns in .NET: Control Flow

Improve your skills in writing simpler and safer code by applying coding practices and design patterns that are affecting control flow. More...

Improving Testability Through Design

This course tackles the issues of designing a complex application so that it can be covered with high quality tests. More...

Share this article