# 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; ` `} ` |

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## Java

`// java program to ilustrate ` `// n arithmetic mean between ` `// A and B ` `import` `java.io.*; ` `import` `java.lang.*; ` `import` `java.util.*; ` ` ` `public` `class` `GFG { ` ` ` ` ` `// insert function for calulating 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); ` ` ` `} ` `} ` |

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## 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 ` |

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## C#

`// C# program to ilustrate ` `// n arithmetic mean between ` `// A and B ` `using System; ` ` ` `public class GFG { ` ` ` ` ` `// insert function for calulating 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 ` |

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## 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. ` `?> ` |

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**Output:**

22 24 26 28 30

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