# Express a number as sum of consecutive numbers

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 <bits/stdc++.h> ` `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<N; last++) ` ` ` `{ ` ` ` `for` `(` `int` `first=0; first<last; first++) ` ` ` `{ ` ` ` `if` `(2*N == (last-first)*(last+first+1)) ` ` ` `{ ` ` ` `cout << N << ` `" = "` `; ` ` ` `printConsecutive(last, first+1); ` ` ` `return` `; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` `cout << ` `"-1"` `; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `n = 12; ` ` ` `findConsecutive(n); ` ` ` `return` `0; ` `} ` |

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## 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); ` ` ` `} ` `} ` |

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## 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. ` |

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## 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 ` |

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## PHP

`<?php ` `// PHP program to print a consecutive ` `// sequence to express N if possible. ` ` ` `// Print consecutive numbers from ` `// last to first ` `function` `printConsecutive(` `$last` `, ` `$first` `) ` `{ ` ` ` `echo` `$first` `++; ` ` ` `for` `(` `$x` `= ` `$first` `; ` `$x` `<= ` `$last` `; ` `$x` `++) ` ` ` `echo` `" + "` `, ` `$x` `; ` `} ` ` ` `function` `findConsecutive(` `$N` `) ` `{ ` ` ` `for` `(` `$last` `= 1; ` `$last` `< ` `$N` `; ` `$last` `++) ` ` ` `{ ` ` ` `for` `(` `$first` `= 0; ` `$first` `< ` `$last` `; ` `$first` `++) ` ` ` `{ ` ` ` `if` `(2 * ` `$N` `== (` `$last` `- ` `$first` `) * ` ` ` `(` `$last` `+ ` `$first` `+ 1)) ` ` ` `{ ` ` ` `echo` `$N` `, ` `" = "` `; ` ` ` `printConsecutive(` `$last` `, ` `$first` `+ 1); ` ` ` `return` `; ` ` ` `} ` ` ` `} ` ` ` `} ` ` ` `echo` `"-1"` `; ` `} ` ` ` ` ` `// Driver Code ` ` ` `$n` `= 12; ` ` ` `findConsecutive(` `$n` `); ` ` ` `// This code is contributed by nitin mittal ` `?> ` |

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Output:

12 = 3 + 4 + 5

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.

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