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Number expressed as sum of five consecutive integers
• Difficulty Level : Basic
• Last Updated : 12 Apr, 2021

Given an integer n, the task is to find whether n can be expressed as sum of five consecutive integer. If yes, find the five consecutive integers, else print “-1”.
Examples:

```Input : n = 15
Output : 1 2 3 4 5
15 = 1 + 2 + 3 + 4 + 5

Input : n = 18
Output : -1```

Method 1: (Brute Force)
The idea is to run a loop from i = 0 to n – 4, check if (i + i+1 + i+2 + i+3 + i+4) is equal to n. Also, check if n is positive or negative and accordingly increment or decrement i by 1.
Below is the implementation of this approach:

## C++

 `// CPP Program to check if a number can``// be expressed as sum of five consecutive``// integers.``#include ``using` `namespace` `std;` `// function to check if a number can be expressed as``// sum of five consecutive integers.``void` `checksum(``int` `n)``{``    ``// if n is 0``    ``if` `(n == 0) {``        ``cout << ``"-2 -1 0 1 2"` `<< endl;``        ``return``;``    ``}` `    ``int` `inc;` `    ``// if n is positive, increment loop by 1.``    ``if` `(n > 0)``        ``inc = 1;` `    ``// if n is negative, decrement loop by 1.``    ``else``        ``inc = -1;` `    ``// Running loop from 0 to n - 4``    ``for` `(``int` `i = 0; i <= n - 4; i += inc) {` `        ``// check if sum of five consecutive``        ``// integer is equal to n.``        ``if` `(i + i + 1 + i + 2 + i + 3 + i + 4 == n) {``            ``cout << i << ``" "` `<< i + 1``                 ``<< ``" "` `<< i + 2``                 ``<< ``" "` `<< i + 3``                 ``<< ``" "` `<< i + 4;``            ``return``;``        ``}``    ``}` `    ``cout << ``"-1"``;``}` `// Driver Program``int` `main()``{``    ``int` `n = 15;``    ``checksum(n);``    ``return` `0;``}`

## Java

 `// Java Program to check if a number can``// be expressed as sum of five consecutive``// integers.``import` `java.io.*;` `class` `GFG {` `    ``// function to check if a number can be``    ``// expressed as sum of five consecutive``    ``// integers.``    ``static` `void` `checksum(``int` `n)``    ``{``        ``// if n is 0``        ``if` `(n == ``0``) {``            ``System.out.println(``"-2 -1 0 1 2"``);``            ``return``;``        ``}``    ` `        ``int` `inc;``    ` `        ``// if n is positive, increment loop by 1.``        ``if` `(n > ``0``)``            ``inc = ``1``;``    ` `        ``// if n is negative, decrement loop by 1.``        ``else``            ``inc = -``1``;``    ` `        ``// Running loop from 0 to n - 4``        ``for` `(``int` `i = ``0``; i <= n - ``4``; i += inc) {``    ` `            ``// check if sum of five consecutive``            ``// integer is equal to n.``            ``if` `(i + i + ``1` `+ i + ``2` `+ i + ``3` `+ i``                                       ``+ ``4` `== n)``            ``{``                ``System.out.print( (i )``                        ``+ ``" "` `+ (i + ``1``)``                        ``+ ``" "` `+ (i + ``2``)``                        ``+ ``" "` `+ (i + ``3``)``                        ``+ ``" "` `+ (i + ``4``));``                ``return``;``            ``}``        ``}``    ` `        ``System.out.println( ``"-1"``);``    ``}``    ` `    ``// Driver Program``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `n = ``15``;``        ``checksum(n);``    ``}``}` `// This code is contributed by anuj_67`

## Python3

 `# Python3 code to check if a number``# can be expressed as sum of five``# consecutive integers.`` ` `# function to check if a number``# can be expressed as sum of five``# consecutive integer.``def` `checksum(n):`` ` `    ``# if n is 0``    ``if` `n ``=``=` `0``:``        ``print``(``"-2 -1 0 1 2"``)``        ``return` `0``         ` `    ``inc ``=` `0`` ` `    ``# if n is positive,``    ``# increment loop by 1.``    ``if` `n > ``0``:``        ``inc ``=` `1``     ` `    ``# if n is negative,``    ``# decrement loop by 1.``    ``else``:``        ``inc ``=` `-``1``     ` `    ``# Running loop from 0 to n - 4``    ``for` `i ``in` `range``(``0``, n``-``3``, inc):``     ` `        ``# check if sum of five consecutive``        ``# integer is equal to n.``        ``if` `i ``+` `i ``+` `1` `+` `i ``+` `2` `+` `i ``+` `3` `+` `i ``+` `4` `=``=` `n:``            ``print``(i, ``" "``, i ``+` `1``, ``" "``, i ``+` `2``, ``" "``, i ``+` `3``, ``" "``, i ``+` `4``)``            ``return` `0``             ` `    ``print``(``"-1"``)``     ` `# Driver Code``n ``=` `15``checksum(n)`

## C#

 `// C# Program to check if a number can``// be expressed as sum of five consecutive``// integers.``using` `System;` `class` `GFG {` `    ``// function to check if a number can be``    ``// expressed as sum of five consecutive``    ``// integers.``    ``static` `void` `checksum(``int` `n)``    ``{``        ``// if n is 0``        ``if` `(n == 0) {``            ``Console.Write(``"-2 -1 0 1 2"``);``            ``return``;``        ``}``    ` `        ``int` `inc;``    ` `        ``// if n is positive, increment loop by 1.``        ``if` `(n > 0)``            ``inc = 1;``    ` `        ``// if n is negative, decrement loop by 1.``        ``else``            ``inc = -1;``    ` `        ``// Running loop from 0 to n - 4``        ``for` `(``int` `i = 0; i <= n - 4; i += inc) {``    ` `            ``// check if sum of five consecutive``            ``// integer is equal to n.``            ``if` `(i + i + 1 + i + 2 + i + 3 + i``                                    ``+ 4 == n)``            ``{``                ``Console.Write( (i )``                        ``+ ``" "` `+ (i + 1)``                        ``+ ``" "` `+ (i + 2)``                        ``+ ``" "` `+ (i + 3)``                        ``+ ``" "` `+ (i + 4));``                ``return``;``            ``}``        ``}``    ` `        ``Console.WriteLine( ``"-1"``);``    ``}``    ` `    ``// Driver Program``    ``public` `static` `void` `Main ()``    ``{``        ``int` `n = 15;``        ``checksum(n);``    ``}``}` `// This code is contributed by anuj_67`

## PHP

 ` 0)``        ``\$inc` `= 1;` `    ``// if n is negative,``    ``// decrement loop by 1.``    ``else``        ``\$inc` `= -1;` `    ``// Running loop from``    ``// 0 to n - 4``    ``for` `(``\$i` `= 0;``         ``\$i` `<= ``\$n` `- 4; ``\$i` `+= ``\$inc``)``    ``{` `        ``// check if sum of five``        ``// consecutive integer``        ``// is equal to n.``        ``if` `(``\$i` `+ ``\$i` `+ 1 + ``\$i` `+ 2 +``            ``\$i` `+ 3 + ``\$i` `+ 4 == ``\$n``)``        ``{``            ``echo` `\$i` `, ``" "` `, ``\$i` `+ 1,``                      ``" "` `, ``\$i` `+ 2,``                      ``" "` `, ``\$i` `+ 3,``                      ``" "` `, ``\$i` `+ 4;``            ``return``;``        ``}``    ``}` `    ``echo` `"-1"``;``}` `// Driver Code``\$n` `= 15;``checksum(``\$n``);` `// This code is contributed``// by ajit``?>`

## Javascript

 ``

Output :

`1 2 3 4 5`

Method 2: (Efficient Approach)
The idea is to check if n is multiple of 5 or not.
Let n is sum of five consecutive integer of k – 2, k-1, k, k + 1, k+2. Therefore,
k-2 + k-1 + k + k+1 + k+2= n
5*k = n
The five numbers will be n/5 – 2, n/5 – 1, n/5, n/5 + 1, n/5 + 2.

Below is the implementation of this approach:

## C++

 `// CPP Program to check if a number can be``// expressed as sum of five consecutive integer.``#include ``using` `namespace` `std;` `// function to check if a number can be``// expressed as sum of five consecutive``// integers.``void` `checksum(``int` `n)``{``    ``// if n is multiple of 5``    ``if` `(n % 5 == 0)``        ``cout << n / 5 - 2 << ``" "``             ``<< n / 5 - 1 << ``" "` `<< n / 5``             ``<< ``" "` `<< n / 5 + 1 << ``" "``             ``<< n / 5 + 2;` `    ``// else print "-1".``    ``else``        ``cout << ``"-1"``;``}` `// Driver Program``int` `main()``{``    ``int` `n = 15;``    ``checksum(n);``    ``return` `0;``}`

## Java

 `// Java Program to check if a number can``// be expressed as sum of five consecutive``// integer.``import` `java.io.*;` `class` `GFG {` `    ``// function to check if a number can``    ``// be expressed as sum of five``    ``// consecutive integers.``    ``static` `void` `checksum(``int` `n)``    ``{``        ``// if n is multiple of 5``        ``if` `(n % ``5` `== ``0``)``            ``System.out.println( (n / ``5` `- ``2``)``                  ``+ ``" "` `+ (n / ``5` `- ``1``) + ``" "``                  ``+ (n / ``5``) + ``" "` `+ (n / ``5``                ``+ ``1` `) + ``" "` `+ (n / ``5` `+ ``2``));``    ` `        ``// else print "-1".``        ``else``            ``System.out.println( ``"-1"``);``    ``}``    ` `    ``// Driver Program``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `n = ``15``;``        ``checksum(n);``    ``}``}` `// This code is contributed by vt_m.`

## Python3

 `# Python3 code to check if a number``# can be expressed as sum of five``# consecutive integer.`` ` `# function to check if a number``# can be expressed as sum of five``# consecutive integers.``def` `checksum(n):``    ``n ``=` `int``(n)``     ` `    ``# if n is multiple of 5``    ``if` `n ``%` `5` `=``=` `0``:``        ``print``(``int``(n ``/` `5` `-` `2``), ``" "``,``         ``int``(n ``/` `5` `-` `1``), ``" "``, ``int``(n ``/` `5``), ``" "``, ``int``(n ``/` `5` `+` `1``), ``" "``, ``int``(n ``/` `5` `+` `2``))``     ` `    ``# else print "-1".``    ``else``:``        ``print``(``"-1"``)``         ` `# Driver Code``n ``=` `15``checksum(n)`

## C#

 `// C# Program to check if a number can``// be expressed as sum of five consecutive``// integer.``using` `System;` `class` `GFG {` `    ``// function to check if a number can``    ``// be expressed as sum of five``    ``// consecutive integers.``    ``static` `void` `checksum(``int` `n)``    ``{``        ``// if n is multiple of 5``        ``if` `(n % 5 == 0)``            ``Console.WriteLine( (n / 5 - 2)``                ``+ ``" "` `+ (n / 5 - 1) + ``" "``                ``+ (n / 5) + ``" "` `+ (n / 5``                ``+ 1 ) + ``" "` `+ (n / 5 + 2));``    ` `        ``// else print "-1".``        ``else``            ``Console.WriteLine( ``"-1"``);``    ``}``    ` `    ``// Driver Program``    ``public` `static` `void` `Main ()``    ``{``        ``int` `n = 15;``        ``checksum(n);``    ``}``}` `// This code is contributed by anuj_67.`

## PHP

 ``

## Javascript

 ``

Output:

`1 2 3 4 5`

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