# 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

```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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++

 `// CPP 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

 `# Python 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` `& ``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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