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Express a number as sum of consecutive numbers
• Difficulty Level : Easy
• Last Updated : 27 Apr, 2021

Given a number N, write a function to express N as sum of two or more consecutive positive numbers. If there is no solution, output -1. If there are multiple solution, then print one of them.
Examples:

```Input : N = 10
Output : 4 + 3 + 2 + 1

Input  : N = 8
Output : -1

Input  : N = 24
Output : 9 + 8 + 7```

```Sum of first n natural numbers = n * (n + 1)/2

Sum of first (n + k) numbers = (n + k) * (n + k + 1)/2

If N is sum of k consecutive numbers, then
following must be true.

N = [(n+k)(n+k+1) - n(n+1)] / 2

OR

2 * N = [(n+k)(n+k+1) - n(n+1)]```

Below is the implementation based on above idea.

## C++

 `// C++ program to print a consecutive sequence``// to express N if possible.``#include ``using` `namespace` `std;` `// Print consecutive numbers from``// last to first``void` `printConsecutive(``int` `last, ``int` `first)``{``    ``cout << first++;``    ``for` `(``int` `x = first; x<= last; x++)``        ``cout << ``" + "` `<< x;``}` `void` `findConsecutive(``int` `N)``{``    ``for` `(``int` `last=1; last

Java

``````
// Java program to print a consecutive sequence
// to express N if possible.
class GfG
{
// Print consecutive numbers from
// last to first
static void printConsecutive(int last, int first)
{
System.out.print(first++);
for (int x = first; x<= last; x++)
System.out.print(" + "+x);
}

static void findConsecutive(int N)
{
for (int last=1; last<N; last++)
{
for (int first=0; first<last; first++)
{
if (2*N == (last-first)*(last+first+1))
{
System.out.printf(N + " = ");
printConsecutive(last, first+1);
return;
}
}
}
System.out.print("-1");
}

// main function
public static void main (String[] args)
{
int n = 12;
findConsecutive(n);
}
}
``````

## Python3

 `# Python3 program to print a consecutive``# sequence to express N if possible.` `# Print consecutive numbers``# from last to first``def` `printConsecutive(last, first):``    ``print` `(first, end ``=` `"")``    ``first ``+``=` `1``    ``for` `x ``in` `range``(first, last ``+` `1``):``        ``print` `(``" +"``, x, end ``=` `"")` `def` `findConsecutive(N):``    ``for` `last ``in` `range``(``1``, N):``        ` `        ``for` `first ``in` `range``(``0``, last):``            ` `            ``if` `2` `*` `N ``=``=` `(last ``-` `first) ``*` `(last ``+` `first ``+` `1``):``                ``print` `(N, ``"= "``, end ``=` `"")``                ``printConsecutive(last, first ``+` `1``)``                ``return``    ``print` `(``"-1"``)` `# Driver code``n ``=` `12``findConsecutive(n)` `# This code is contributed by Shreyanshi Arun.`

## C#

 `// C# program to print a consecutive sequence``// to express N if possible.``using` `System;` `class` `GfG``{``    ``// Print consecutive numbers from``    ``// last to first``    ``static` `void` `printConsecutive(``int` `last, ``int` `first)``    ``{``        ``Console.Write(first++);``        ``for` `(``int` `x = first; x <= last; x++)``            ``Console.Write(``" + "``+x);``    ``}``    ` `    ``static` `void` `findConsecutive(``int` `N)``    ``{``        ``for` `(``int` `last = 1; last < N; last++)``        ``{``            ``for` `(``int` `first = 0; first < last; first++)``            ``{``                ``if` `(2 * N == (last - first)``                    ``* (last + first + 1))``                ``{``                    ``Console.Write(N + ``" = "``);``                    ``printConsecutive(last, first + 1);``                    ``return``;``                ``}``            ``}``        ``}``        ``Console.Write(``"-1"``);``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `Main ()``    ``{``        ``int` `n = 12;``        ``findConsecutive(n);``    ``}``}` `// This code is contributed by vt_m`

## PHP

 ``

## Javascript

 ``

Output:

`12 = 3 + 4 + 5`

Reference :
https://math.stackexchange.com/questions/139842/in-how-many-ways-can-a-number-be-expressed-as-a-sum-of-consecutive-numbers
This article is contributed by Roshni Agarwal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.