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Find N Arithmetic Means between A and B

• Difficulty Level : Medium
• Last Updated : 28 Nov, 2019

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
20 22 24 26 28 30 32

Input : A = 5  B = 35  N = 5
Output : 10 15 20 25 30
```

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach :
Let A1, A2, A3, A4……An be N Arithmetic Means between two given numbers A and B . Then A, A1, A2 ….. An, 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 ``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

 ``
Output:
```22 24 26 28 30
```

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