Open in App
Not now

Find the sum of first N terms of the series 2×3 + 4×4 + 6×5 + 8×6 + …

• Difficulty Level : Easy
• Last Updated : 25 May, 2022

Given an integer N. The task is to find the sum upto N terms of the given series:

2×3 + 4×4 + 6×5 + 8×6 + … + upto n terms

Examples:

Input : N = 5
Output : Sum = 170

Input : N = 10
Output : Sum = 990

Let the N-th term of the series be tN
t1 = 2 × 3 = (2 × 1)(1 + 2)
t2 = 4 × 4 = (2 × 2)(2 + 2)
t3 = 6 × 5 = (2 × 3)(3 + 2)
t4 = 8 × 6 = (2 × 4)(4 + 2)

tN = (2 × N)(N + 2)
The sum of n terms of the series,

 Sn = t1 + t2 +... + tn
=======

Below is the implementation of above approach:

C++

 // C++ program to find sum upto // N term of the series:  // 2 × 3 + 4 × 4 + 6 × 5 + 8 × 6 + ...  #include using namespace std;   // calculate sum upto N term of series  void Sum_upto_nth_Term(int n)  {     int r = n * (n + 1) *                  (2 * n + 7) / 3;     cout << r; }   // Driver code  int main() {     int N = 5;     Sum_upto_nth_Term(N) ;     return 0; }

Java

 // Java program to find sum upto // N term of the series:    import java.io.*;   class GFG { // calculate sum upto N term of series  static void Sum_upto_nth_Term(int n)  {     int r = n * (n + 1) *                  (2 * n + 7) / 3;     System.out.println(r); }   // Driver code     public static void main (String[] args) {     int N = 5;     Sum_upto_nth_Term(N);     } }

Python3

 # Python program to find sum upto N term of the series: # 2 × 3 + 4 × 4 + 6 × 5 + 8 × 6 + ...   # calculate sum upto N term of series def Sum_upto_nth_Term(n):     return n * (n + 1) * (2 * n + 7) // 3   # Driver code N = 5 print(Sum_upto_nth_Term(N))

C#

 // C# program to find sum upto // N term of the series:  // 2 × 3 + 4 × 4 + 6 × 5 + 8 × 6 + ...    using System;   class GFG { // calculate sum upto N term of series  static void Sum_upto_nth_Term(int n)  {     int r = n * (n + 1) *                  (2 * n + 7) / 3;     Console.Write(r); }   // Driver code  public static void Main() {     int N = 5;     Sum_upto_nth_Term(N); } }   // This code is contributed  // by Akanksha Rai(Abby_akku)

PHP

 

Javascript

 

Output:

170

Time Complexity: O(1), it is a constant.
Auxiliary Space: O(1), no extra space is required.

My Personal Notes arrow_drop_up
Related Articles