# Find if a number is part of AP whose first element and difference are given

Given three non-negative integers a, d and x. Here, a is the first element, d is the difference of an AP (Arithmetic Progression). We need to find if x is part of the given AP or not.

**Examples :**

Input : a = 1, d = 3, x = 7 Output : Yes 7 is part of given AP, 1 + 3 + 3 = 7 Input : a = 10, d = 0, x = 10 Output : Yes

Firstly, in case d = 0, we should output Yes if a = x else answer is No. For non-zero d, if x belongs to sequence x = a + n * d where n is non-negative integer, only if (n – a) / d is non-negative integer.

## C++

`// C++ program to check if x exist` `// or not in the given AP.` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// returns yes if exist else no.` `bool` `isMember(` `int` `a, ` `int` `d, ` `int` `x)` `{` ` ` `// If difference is 0, then x must` ` ` `// be same as a.` ` ` `if` `(d == 0)` ` ` `return` `(x == a);` ` ` `// Else difference between x and a` ` ` `// must be divisible by d.` ` ` `return` `((x - a) % d == 0 && (x - a) / d >= 0);` `}` `// Driver code.` `int` `main()` `{` ` ` `int` `a = 1, x = 7, d = 3;` ` ` `if` `(isMember(a, d, x))` ` ` `cout << ` `"Yes"` `;` ` ` `else` ` ` `cout << ` `"No"` `;` ` ` `return` `0;` `}` |

## Java

`// Java program to check if x exist` `// or not in the given AP.` `class` `GFG {` ` ` `// returns yes if exist else no.` ` ` `static` `boolean` `isMember(` `int` `a, ` `int` `d, ` `int` `x)` ` ` `{` ` ` `// If difference is 0, then x must` ` ` `// be same as a.` ` ` `if` `(d == ` `0` `)` ` ` `return` `(x == a);` ` ` `// Else difference between x and a` ` ` `// must be divisible by d.` ` ` `return` `((x - a) % d == ` `0` `&& (x - a) / d >= ` `0` `);` ` ` `}` ` ` `// Driver code.` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `a = ` `1` `, x = ` `7` `, d = ` `3` `;` ` ` `if` `(isMember(a, d, x))` ` ` `System.out.println(` `"Yes"` `);` ` ` `else` ` ` `System.out.println(` `"No"` `);` ` ` `}` `}` `// This code is contributed by Nikita Tiwari` |

## Python3

`# Python3 code to check if x exist` `# or not in the given AP.` `def` `isMember(a, d, x):` ` ` ` ` `# If difference is 0, then x` ` ` `# must be same as a.` ` ` `if` `d ` `=` `=` `0` `:` ` ` `return` `x ` `=` `=` `a` ` ` ` ` `# Else difference between x` ` ` `# and a must be divisible by d.` ` ` `return` `((x ` `-` `a) ` `%` `d ` `=` `=` `0` `and` ` ` `int` `((x ` `-` `a) ` `/` `d) >` `=` `0` `)` `# Driver code` `a ` `=` `1` `x ` `=` `7` `d ` `=` `3` `if` `isMember(a, d, x):` ` ` `print` `( ` `"Yes"` `)` `else` `:` ` ` `print` `(` `"No"` `)` `# This code is contributed by "Abhishek Sharma 44"` |

## C#

`// C# program to check if x exist` `// or not in the given AP.` `using` `System;` `class` `GFG {` ` ` `// returns yes if exist else no.` ` ` `static` `bool` `isMember(` `int` `a, ` `int` `d, ` `int` `x)` ` ` `{` ` ` `// If difference is 0, then x must` ` ` `// be same as a.` ` ` `if` `(d == 0)` ` ` `return` `(x == a);` ` ` `// Else difference between x and a` ` ` `// must be divisible by d.` ` ` `return` `((x - a) % d == 0 && (x - a) / d >= 0);` ` ` `}` ` ` `// Driver code.` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `a = 1, x = 7, d = 3;` ` ` `if` `(isMember(a, d, x))` ` ` `Console.WriteLine(` `"Yes"` `);` ` ` `else` ` ` `Console.WriteLine(` `"No"` `);` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to check ` `// if x exist or not in` `// the given AP.` `// returns yes if exist` `// else no.` `function` `isMember(` `$a` `, ` `$d` `, ` `$x` `)` `{` ` ` `// If difference is 0, then` ` ` `// x must be same as a` ` ` `if` `(` `$d` `== 0)` ` ` `return` `(` `$x` `== ` `$a` `);` ` ` `// Else difference between x` `// and a must be divisible by d.` `return` `((` `$x` `- ` `$a` `) % ` `$d` `== 0 &&` ` ` `(` `$x` `- ` `$a` `) / ` `$d` `>= 0);` `}` `// Driver code.` `$a` `= 1; ` `$x` `= 7; ` `$d` `= 3;` `if` `(isMember(` `$a` `, ` `$d` `, ` `$x` `))` ` ` `echo` `"Yes"` `;` `else` ` ` `echo` `"No"` `;` `// This code is contributed by aj_36` `?>` |

## Javascript

`<script>` ` ` `// Javascript program to check if x exist` ` ` `// or not in the given AP.` ` ` ` ` `// returns yes if exist else no.` ` ` `function` `isMember(a, d, x)` ` ` `{` ` ` `// If difference is 0, then x must` ` ` `// be same as a.` ` ` `if` `(d == 0)` ` ` `return` `(x == a);` ` ` `// Else difference between x and a` ` ` `// must be divisible by d.` ` ` `return` `((x - a) % d == 0 && (x - a) / d >= 0);` ` ` `}` ` ` ` ` `let a = 1, x = 7, d = 3;` ` ` `if` `(isMember(a, d, x))` ` ` `document.write(` `"Yes"` `);` ` ` `else` ` ` `document.write(` `"No"` `);` ` ` ` ` `// This code is contributed by divyeshrabadiya07.` `</script>` |

**Output :**

Yes