# Find the sum of elements of the Matrix generated by the given rules

Given three integers A, B and R, the task is to find the sum of all the elements of the matrix generated by the given rules:

1. The first row will contain a single element which is A and the rest of the elements will be 0.
2. The next row will contain two elements all of which are (A + B) and the rest are 0s.
3. Third row will contain (A + B + B) three times and the rest are 0s.
4. …..
5. The matrix will contain only R rows.

For example, if A = 5, B = 3 and R = 3 then the matrix will be:
5 0 0
8 8 0
11 11 11

Examples:

Input: A = 5, B = 3, R = 3
Output: 54
5 + 8 + 8 + 11 + 11 + 11 = 54

Input: A = 7, B = 56, R = 1
Output: 7

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

Approach: Initialise sum = 0 and for every 1 ≤ i ≤ R update sum = sum + (i * A). After every iteration update A = A + B. Print the final sum in the end.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` ` `  `// Function to return the required sum ` `int` `sum(``int` `A, ``int` `B, ``int` `R) ` `{ ` ` `  `    ``// To store the sum ` `    ``int` `sum = 0; ` ` `  `    ``// For every row ` `    ``for` `(``int` `i = 1; i <= R; i++) { ` ` `  `        ``// Update the sum as A appears i number ` `        ``// of times in the current row ` `        ``sum = sum + (i * A); ` ` `  `        ``// Update A for the next row ` `        ``A = A + B; ` `    ``} ` ` `  `    ``// Return the sum ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `A = 5, B = 3, R = 3; ` `    ``cout << sum(A, B, R); ` ` `  `    ``return` `0; ` `} `

## Java

 `// JAVA implementation of the approach ` `import` `java.util.*; ` `import` `java.lang.*; ` `import` `java.io.*; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the required sum ` `static` `int` `sum(``int` `A, ``int` `B, ``int` `R) ` `{ ` ` `  `    ``// To store the sum ` `    ``int` `sum = ``0``; ` ` `  `    ``// For every row ` `    ``for` `(``int` `i = ``1``; i <= R; i++)  ` `    ``{ ` ` `  `        ``// Update the sum as A appears i number ` `        ``// of times in the current row ` `        ``sum = sum + (i * A); ` ` `  `        ``// Update A for the next row ` `        ``A = A + B; ` `    ``} ` ` `  `    ``// Return the sum ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main (String[] args)  ` `              ``throws` `java.lang.Exception ` `{ ` `    ``int` `A = ``5``, B = ``3``, R = ``3``; ` `     `  `    ``System.out.print(sum(A, B, R)); ` `} ` `} ` ` `  `// This code is contributed by nidhiva `

## Python3

 `# Python3 implementation of the approach ` ` `  `# Function to return the required ssum ` `def` `Sum``(A, B, R): ` ` `  `    ``# To store the ssum ` `    ``ssum ``=` `0` ` `  `    ``# For every row ` `    ``for` `i ``in` `range``(``1``, R ``+` `1``): ` ` `  `        ``# Update the ssum as A appears i number ` `        ``# of times in the current row ` `        ``ssum ``=` `ssum ``+` `(i ``*` `A) ` ` `  `        ``# Update A for the next row ` `        ``A ``=` `A ``+` `B ` ` `  `    ``# Return the ssum ` `    ``return` `ssum ` ` `  `# Driver code ` `A, B, R ``=` `5``, ``3``, ``3` `print``(``Sum``(A, B, R)) ` ` `  `# This code is contributed by Mohit Kumar `

## C#

 `// C# implementation of the approach ` `using` `System; ` ` `  `class` `GFG ` `{ ` ` `  `// Function to return the required sum ` `static` `int` `sum(``int` `A, ``int` `B, ``int` `R) ` `{ ` ` `  `    ``// To store the sum ` `    ``int` `sum = 0; ` ` `  `    ``// For every row ` `    ``for` `(``int` `i = 1; i <= R; i++)  ` `    ``{ ` ` `  `        ``// Update the sum as A appears i number ` `        ``// of times in the current row ` `        ``sum = sum + (i * A); ` ` `  `        ``// Update A for the next row ` `        ``A = A + B; ` `    ``} ` ` `  `    ``// Return the sum ` `    ``return` `sum; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main ()  ` `{ ` `    ``int` `A = 5, B = 3, R = 3; ` `     `  `    ``Console.Write(sum(A, B, R)); ` `} ` `} ` ` `  `// This code is contributed by anuj_67.. `

Output:

```54
```

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Improved By : mohit kumar 29, nidhiva, vt_m

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