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++

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// CPP 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;
}

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Java

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// 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

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Python3

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# 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"

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C#

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// 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.

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PHP

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<?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
?>

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Output :

Yes


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Improved By : jit_t