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# Sum of the series 3, 20, 63, 144, ……

Find the sum of first n terms of the given series:

3, 20, 63, 144, .....

Examples:

Input : n = 2
Output : 23

Input : n =4
Output : 230

Approach
First, we have to find the general term (Tn) of the given series.

series can we written in the following way also:
(3 * 1^2), (5 * 2^2), (7 * 3^2), (9 * 4^2), .......up t n terms
Tn = (General term of series 3, 5, 7, 9 ....) X (General term of series 1^2, 2^2, 3^2, 4^2 ....)
Tn = (3 + (n-1) * 2) X ( n^2 )
Tn = 2*n^3 + n^2

We can write the sum of the series in the following ways:

 Sn = 3 + 20 + 63 + 144 + ........up to the n terms [Tex]$$Sn = 2 \times \sum_{n=1}^{n} n^{3} + \sum_{n=1}^{n} n^{2}$$[/Tex]Sn = 2 * (sum of n terms of n^3 ) + (sum of n terms of n^2)

Following are the formulas of sum of n terms of n^3 and n^2 :  Below is the implementation of the above approach:

## C++

 // C++ program to find the sum of n terms#include using namespace std;int calculateSum(int n){    return (2 * pow((n * (n + 1) / 2), 2)) +           ((n * (n + 1) * (2 * n + 1)) / 6);}int main(){    int n = 4;    cout << "Sum = " << calculateSum(n) << endl;    return 0;}

## Java

 // Java program to find the sum of n termsimport java.io.*; public class GFG{    static int calculateSum(int n)    {        return (int)((2 * Math.pow((n * (n + 1) / 2), 2))) +               ((n * (n + 1) * (2 * n + 1)) / 6);    }         public static void main (String[] args) {             int n = 4;        System.out.println("Sum = " +  calculateSum(n));         }}// This code is contributed by Raj

## Python3

 # Python3 program to find the sum of n terms def calculateSum(n):    return ((2 * (n * (n + 1) / 2)**2) +           ((n * (n + 1) * (2 * n + 1)) / 6))     #Driver code n = 4print("Sum =",calculateSum(n)) # this code is contributed by Shashank_Sharma

## C#

 // C# program to find the sum of n termsusing System; class GFG{static int calculateSum(int n){    return (int)((2 * Math.Pow((n * (n + 1) / 2), 2))) +                     ((n * (n + 1) * (2 * n + 1)) / 6);} // Driver Codepublic static void Main (){    int n = 4;    Console.WriteLine("Sum = " + calculateSum(n));}} // This code is contributed by anuj_67

## PHP

 

## Javascript

 

Output:

Sum = 230

Time Complexity: O(1)

Auxiliary Space: O(1)

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