Given three integers A, B and N the task is to find N Geometric means between A and B. WE basically need to insert N terms in a Geometric progression. where A and B are first and last terms. **Examples:**

Input : A = 2 B = 32 N = 3 Output : 4 8 16 the geometric progression series as 2,4, 8, 16, 32 Input : A = 3 B = 81 N = 2 Output : 9 27

**Approach :**

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

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

Then Here R is the common ratio

B = A*R^{N+1}

R^{N+1} = B/A **R = (B/A) ^{1/(N+1)}**

Now we have the value of R

And also we have the value of the first term A

G

_{1}= AR

^{1}= A * (B/A)

^{1/(N+1)}

G

_{2}= AR

^{2}= A * (B/A)

^{2/(N+1)}

G

_{3}= AR

^{3}= A * (B/A)

^{3/(N+1)}

.

.

.

**G**

_{N}= AR^{N}= A * (B/A)^{N/(N+1)}## C++

`// C++ program to find n geometric means` `// between A and B` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Prints N geometric means between` `// A and B.` `void` `printGMeans(` `int` `A, ` `int` `B, ` `int` `N)` `{` ` ` `// calculate common ratio(R)` ` ` `float` `R = (` `float` `)` `pow` `(` `float` `(B / A),` ` ` `1.0 / (` `float` `)(N + 1));` ` ` ` ` `// for finding N the Geometric` ` ` `// mean between A and B` ` ` `for` `(` `int` `i = 1; i <= N; i++)` ` ` `cout << A * ` `pow` `(R, i) <<` `" "` `; ` `}` `// Driver code to test above` `int` `main()` `{` ` ` `int` `A = 3, B = 81, N = 2;` ` ` `printGMeans(A, B, N); ` ` ` `return` `0;` `}` |

## Java

`// java program to illustrate` `// n geometric 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` `printGMeans(` `int` `A, ` `int` `B, ` `int` `N)` ` ` `{ ` ` ` `// Finding the value of R Common ration` ` ` `float` `R = (` `float` `)Math.pow((` `float` `)(B / A),` ` ` `1.0` `/ (` `float` `)(N + ` `1` `));` ` ` ` ` `// for finding N the Geometric` ` ` `// mean between A and B` ` ` `for` `(` `int` `i = ` `1` `; i <= N; i++)` ` ` `System.out.print(A * Math.pow(R, i) + ` `" "` `);` ` ` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `A = ` `3` `, B = ` `81` `, N = ` `2` `;` ` ` `printGMeans(A, B, N);` ` ` `}` `}` |

## Python3

`# Python3 program to find` `# n geometric means` `# between A and B` `import` `math` `# Prints N geometric means` `# between A and B.` `def` `printGMeans(A, B, N):` ` ` ` ` `# calculate` ` ` `# common ratio(R)` ` ` `R ` `=` `(math.` `pow` `((B ` `/` `A),` ` ` `1.0` `/` `(N ` `+` `1` `)));` ` ` ` ` `# for finding N the` ` ` `# Geometric mean` ` ` `# between A and B` ` ` `for` `i ` `in` `range` `(` `1` `, N ` `+` `1` `):` ` ` `print` `(` `int` `(A ` `*` `math.` `pow` `(R, i)),` ` ` `end ` `=` `" "` `);` `# Driver Code` `A ` `=` `3` `;` `B ` `=` `81` `;` `N ` `=` `2` `;` `printGMeans(A, B, N);` ` ` `# This code is contributed` `# by mits` |

## C#

`// C# program to illustrate` `// n geometric mean between` `// A and B` `using` `System;` `public` `class` `GFG {` ` ` `// insert function for calculating the means` ` ` `static` `void` `printGMeans(` `int` `A, ` `int` `B, ` `int` `N)` ` ` `{` ` ` ` ` `// Finding the value of R Common ration` ` ` `float` `R = (` `float` `)Math.Pow((` `float` `)(B / A),` ` ` `1.0 / (` `float` `)(N + 1));` ` ` ` ` `// for finding N the Geometric` ` ` `// mean between A and B` ` ` `for` `(` `int` `i = 1; i <= N; i++)` ` ` `Console.Write(A * Math.Pow(R, i) + ` `" "` `);` ` ` ` ` `}` ` ` `// Driver code` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `A = 3, B = 81, N = 2;` ` ` ` ` `printGMeans(A, B, N);` ` ` `}` `}` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find` `// n geometric means` `// between A and B` `// Pr$s N geometric means` `// between A and B.` `function` `printGMeans(` `$A` `, ` `$B` `, ` `$N` `)` `{` ` ` ` ` `// calculate common ratio(R)` ` ` `$R` `= pow((` `$B` `/ ` `$A` `),` ` ` `1.0 / (` `$N` `+ 1));` ` ` ` ` `// for finding N the Geometric` ` ` `// mean between A and B` ` ` `for` `(` `$i` `= 1; ` `$i` `<= ` `$N` `; ` `$i` `++)` ` ` `echo` `$A` `* pow(` `$R` `, ` `$i` `) ,` `" "` `;` `}` ` ` `// Driver Code` ` ` `$A` `= 3;` ` ` `$B` `= 81;` ` ` `$N` `= 2;` ` ` `printGMeans(` `$A` `, ` `$B` `, ` `$N` `);` ` ` `// This code is contributed by anuj_67.` `?>` |

## Javascript

`<script>` `// JavaScript program to illustrate` `// n geometric mean between` `// A and B` ` ` `// insert function for calculating the means` ` ` `function` `printGMeans(A, B, N)` ` ` `{ ` ` ` `// Finding the value of R Common ration` ` ` `let R = Math.pow((B / A),` ` ` `1.0 / (N + 1));` ` ` ` ` `// for finding N the Geometric` ` ` `// mean between A and B` ` ` `for` `(let i = 1; i <= N; i++)` ` ` `document.write(A * Math.pow(R, i) + ` `" "` `);` ` ` ` ` `}` `// Driver Code` ` ` `let A = 3, B = 81, N = 2;` ` ` `printGMeans(A, B, N);` `// This code is contributed by code_hunt.` `</script>` |

**Output :**

9 27

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