# Find if the given number is present in the infinite sequence or not

Given three integers A, B and C. In an infinite sequence, A is the first number, C is the common difference (Si – Si – 1 = C). The task is to check if the number B will appear in the sequence or not.
Examples:

Input: A = 1, B = 7, C = 3
Output: Yes
The sequence will be 1, 4, 7, 10, …
Input: A = 1, B = -4, C = 5
Output: No

Approach: There are two cases:

1. When C = 0, print Yes if A = B else No as the sequence will consist only the number A
2. When C > 0, for any non-negative integer k the equation B = A + k * C must be satisfied i.e. (B – A) / C must be a non-negative integer.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach` `#include ` `using` `namespace` `std;`   `// Function that returns true if` `// the sequence will contain B` `bool` `doesContainB(``int` `a, ``int` `b, ``int` `c)` `{` `    ``if` `(a == b)` `        ``return` `true``;`   `    ``if` `((b - a) * c > 0 && (b - a) % c == 0)` `        ``return` `true``;`   `    ``return` `false``;` `}`   `// Driver code` `int` `main()` `{` `    ``int` `a = 1, b = 7, c = 3;`   `    ``if` `(doesContainB(a, b, c))` `        ``cout << ``"Yes"``;` `    ``else` `        ``cout << ``"No"``;`   `    ``return` `0;` `}`

## Java

 `// Java implementation of the approach` `class` `GFG ` `{`   `    ``// Function that returns true if ` `    ``// the sequence will contain B ` `    ``static` `boolean` `doesContainB(``int` `a, ``int` `b, ``int` `c) ` `    ``{` `        ``if` `(a == b) ` `        ``{` `            ``return` `true``;` `        ``}`   `        ``if` `((b - a) * c > ``0` `&& (b - a) % c == ``0``) ` `        ``{` `            ``return` `true``;` `        ``}`   `        ``return` `false``;` `    ``}`   `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{` `        ``int` `a = ``1``, b = ``7``, c = ``3``;`   `        ``if` `(doesContainB(a, b, c)) ` `        ``{` `            ``System.out.println(``"Yes"``);` `        ``} ` `        ``else` `        ``{` `            ``System.out.println(``"No"``);` `        ``}` `    ``}` `}`   `// This code contributed by Rajput-Ji`

## Python3

 `# Python3 implementation of the approach`   `# Function that returns true if` `# the sequence will contain B` `def` `doesContainB(a, b, c):` `    ``if` `(a ``=``=` `b):` `        ``return` `True`   `    ``if` `((b ``-` `a) ``*` `c > ``0` `and` `(b ``-` `a) ``%` `c ``=``=` `0``):` `        ``return` `True`   `    ``return` `False`   `# Driver code` `if` `__name__ ``=``=` `'__main__'``:` `    ``a, b, c ``=` `1``, ``7``, ``3`   `    ``if` `(doesContainB(a, b, c)):` `        ``print``(``"Yes"``)` `    ``else``:` `        ``print``(``"No"``)`   `# This code is contributed by 29AjayKumar`

## C#

 `// C# implementation of the approach` `using` `System;`   `class` `GFG ` `{`   `    ``// Function that returns true if ` `    ``// the sequence will contain B ` `    ``static` `bool` `doesContainB(``int` `a, ``int` `b, ``int` `c) ` `    ``{` `        ``if` `(a == b) ` `        ``{` `            ``return` `true``;` `        ``}`   `        ``if` `((b - a) * c > 0 && (b - a) % c == 0) ` `        ``{` `            ``return` `true``;` `        ``}`   `        ``return` `false``;` `    ``}`   `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{` `        ``int` `a = 1, b = 7, c = 3;`   `        ``if` `(doesContainB(a, b, c)) ` `        ``{` `            ``Console.WriteLine(``"Yes"``);` `        ``} ` `        ``else` `        ``{` `            ``Console.WriteLine(``"No"``);` `        ``}` `    ``}` `}`   `/* This code contributed by PrinciRaj1992 */`

## PHP

 ` 0 && ` `        ``(``\$b` `- ``\$a``) % ``\$c` `== 0)` `        ``return` `true;`   `    ``return` `false;` `}`   `// Driver code` `\$a` `= 1; ``\$b` `= 7; ``\$c` `= 3;`   `if` `(doesContainB(``\$a``, ``\$b``, ``\$c``))` `    ``echo` `"Yes"``;` `else` `    ``echo` `"No"``;`   `// This code is contributed` `// by Akanksha Rai` `?>`

## Javascript

 ``

Output:

`Yes`

Time Complexity: O(1), since there is only basic arithmetic which takes constant time.
Auxiliary Space: O(1), since no extra space has been taken.

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