# Find N Geometric Means between A and B

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
```

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

Approach :
Let A1, G2, G3, G4……Gn be N geometric Means between two given numbers A and B . Then A, G1, G2 ….. Gn, 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*RN+1
RN+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
G1 = AR1 = A * (B/A)1/(N+1)
G2 = AR2 = A * (B/A)2/(N+1)
G3 = AR3 = A * (B/A)3/(N+1)
.
.
.
GN = ARN = A * (B/A)N/(N+1)

## C++

 `// C++ program to find n geometric means ` `// between A and B ` `#include ` `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

 ` `

Output :

```9 27
```

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