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Find if a number is part of AP whose first element and difference are given
• Difficulty Level : Easy
• Last Updated : 09 Apr, 2021

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``?>`

## Javascript

 ``

Output :

`Yes`

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