Find if a number is part of AP whose first element and difference are given

27 Sep, 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 the 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) / d is non-negative integer. 
C++
Java
Python3
C#
PHP
Javascript
// C++ 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;}
// 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 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 codea = 1x = 7d = 3 if isMember(a, d, x):    print( "Yes")else:    print("No") # This code is contributed by "Abhishek Sharma 44"
// 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// 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?>
<script>    // Javascript 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);    }         let a = 1, x = 7, d = 3;    if (isMember(a, d, x))        document.write("Yes");    else        document.write("No");         // This code is contributed by divyeshrabadiya07.</script>
Output : 
Yes
 
jit_t
asheshkumar
divyeshrabadiya07
shubhambonde2000
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