# 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 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) / c is non-negative integer.

## C++

 `// C++ program to check if x exist` `// or not in the given AP.` `#include ` `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

 `= 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` `?>`

Output :

```Yes

```

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