# Find N Arithmetic Means between A and B

Given three integers A, B and N the task is to find N Arithmetic means between A and B. We basically need to insert N terms in an Arithmetic progression. where A and B are first and last terms.

Examples:

Input : A = 20 B = 32 N = 5 Output : 22 24 26 28 30 The Arithmetic progression series as 2022 24 26 28 3032 Input : A = 5 B = 35 N = 5 Output : 10 15 20 25 30

**Approach :**

Let A_{1}, A_{2}, A_{3}, A_{4}……A_{n} be N Arithmetic Means between two given numbers A and B . Then A, A_{1}, A_{2} ….. A_{n}, B will be in Arithmetic Progression .

Now B = (N+2)^{th} term of the Arithmetic progression .

So :

Finding the (N+2)^{th} term of the Arithmetic progression Series

where d is the Common Difference

B = A + (N + 2 – 1)d

B – A = (N + 1)d

So the Common Difference d is given by.

**d = (B – A) / (N + 1)**

So now we have the value of** A **and the value of the **common difference(d)**,

now we can find all the N Arithmetic Means between A and B.

## C++

`// C++ program to find n arithmetic ` `// means between A and B` `#include <bits/stdc++.h>` `using` `namespace` `std;` ` ` `// Prints N arithmetic means between` `// A and B.` `void` `printAMeans(` `int` `A, ` `int` `B, ` `int` `N)` `{` ` ` `// calculate common difference(d)` ` ` `float` `d = (` `float` `)(B - A) / (N + 1);` ` ` ` ` `// for finding N the arithmetic ` ` ` `// mean between A and B` ` ` `for` `(` `int` `i = 1; i <= N; i++) ` ` ` `cout << (A + i * d) <<` `" "` `; ` `}` ` ` `// Driver code to test above ` `int` `main()` `{` ` ` `int` `A = 20, B = 32, N = 5;` ` ` `printAMeans(A, B, N); ` ` ` `return` `0;` `}` |

## Java

`// java program to illustrate` `// n arithmetic mean between ` `// A and B` `import` `java.io.*;` `import` `java.lang.*;` `import` `java.util.*;` ` ` `public` `class` `GFG {` ` ` ` ` `// insert function for calculating the means` ` ` `static` `void` `printAMeans(` `int` `A, ` `int` `B, ` `int` `N)` ` ` `{ ` ` ` `// Finding the value of d Common difference` ` ` `float` `d = (` `float` `)(B - A) / (N + ` `1` `);` ` ` ` ` `// for finding N the Arithmetic ` ` ` `// mean between A and B` ` ` `for` `(` `int` `i = ` `1` `; i <= N; i++) ` ` ` `System.out.print((A + i * d) + ` `" "` `);` ` ` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `A = ` `20` `, B = ` `32` `, N = ` `5` `;` ` ` `printAMeans(A, B, N);` ` ` `}` `}` |

## Python3

`# Python3 program to find n arithmetic` `# means between A and B` ` ` `# Prints N arithmetic means ` `# between A and B.` `def` `printAMeans(A, B, N):` ` ` ` ` `# Calculate common difference(d)` ` ` `d ` `=` `(B ` `-` `A) ` `/` `(N ` `+` `1` `)` ` ` ` ` `# For finding N the arithmetic ` ` ` `# mean between A and B` ` ` `for` `i ` `in` `range` `(` `1` `, N ` `+` `1` `): ` ` ` `print` `(` `int` `(A ` `+` `i ` `*` `d), end ` `=` `" "` `) ` ` ` `# Driver code` `A ` `=` `20` `; B ` `=` `32` `; N ` `=` `5` `printAMeans(A, B, N) ` ` ` `# This code is contributed by Smitha Dinesh Semwal` |

## C#

`// C# program to illustrate` `// n arithmetic mean between ` `// A and B` `using System;` ` ` `public class GFG {` ` ` ` ` `// insert function for calculating the means` ` ` `static void printAMeans(int A, int B, int N)` ` ` `{ ` ` ` `// Finding the value of d Common difference` ` ` `float d = (float)(B - A) / (N + 1);` ` ` ` ` `// for finding N the Arithmetic ` ` ` `// mean between A and B` ` ` `for (int i = 1; i <= N; i++) ` ` ` `Console.Write((A + i * d) + " ");` ` ` ` ` `}` ` ` ` ` `// Driver code` ` ` `public static void Main()` ` ` `{` ` ` `int A = 20, B = 32, N = 5;` ` ` `printAMeans(A, B, N);` ` ` `}` `}` `// Contributed by vt_m` |

## PHP

`<?php` `// PHP program to find n arithmetic ` `// means between A and B` ` ` `// Prints N arithmetic means ` `// between A and B.` `function` `printAMeans(` `$A` `, ` `$B` `, ` `$N` `)` `{` ` ` ` ` `// calculate common` ` ` `// difference(d)` ` ` `$d` `= (` `$B` `- ` `$A` `) / (` `$N` `+ 1);` ` ` ` ` `// for finding N the arithmetic ` ` ` `// mean between A and B` ` ` `for` `(` `$i` `= 1; ` `$i` `<= ` `$N` `; ` `$i` `++) ` ` ` `echo` `(` `$A` `+ ` `$i` `* ` `$d` `) ,` `" "` `; ` `}` ` ` ` ` `// Driver Code ` ` ` `$A` `= 20; ` `$B` `= 32; ` ` ` `$N` `= 5;` ` ` `printAMeans(` `$A` `, ` `$B` `, ` `$N` `);` ` ` `// This code is Contributed by vt_m.` `?>` |

**Output:**

22 24 26 28 30

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