# Find the Sum of the series 1, 2, 3, 6, 9, 18, 27, 54, … till N terms

Given a number N, the task is to find the sum of the below series till N terms. Examples:

Input: N = 8
Output: 201
1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 + 81 = 201

Input: N = 12
Output: 1821
1 + 2 + 3 + 6 + 9 + 18 + 27 + 54 + 81 + 162 + 243 + 486 + 729 = 1821

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

Approach: From the given series, find the formula for Nth term:

1st term = 1
2nd term = 2 = 2 * 1
3rd term = 3 = 3/2 * 2
4th term = 6 = 2 * 3
5th term = 9 = 3/2 * 6
6th term = 18 = 2 * 9
.
.
Nth term = [2 * (N-1)th term], if N is even
[3/2 * (N-1)th term], if N is odd


Therefore:

Nth term of the series Then iterate over numbers in the range [1, N] to find all the terms using the above formula and compute their sum.

Approach: By observing the pattern in the given series, the next numbers of the series are alternatively multiplied by 2 and 3/2.

Below is the implementation of the above approach:

## C++

 // C++ program for the above series  #include  using namespace std;     // Function to find the sum of series  void printSeriesSum(int N)  {      double sum = 0;         int a = 1;      int cnt = 0;         // Flag to find the multiplicating      // factor.. i.e, by 2 or 3/2      bool flag = true;         // First term      sum += a;         while (cnt < N) {             int nextElement;             // If flag is true, multiply by 2          if (flag) {              nextElement = a * 2;              sum += nextElement;              flag = !flag;          }             // If flag is false, multiply by 3/2          else {              nextElement = a * 3 / 2;              sum += nextElement;              flag = !flag;          }             // Update the previous element          // to nextElement          a = nextElement;          cnt++;      }         // Print the sum      cout << sum << endl;  }     // Driver Code  int main()  {         int N = 8;         printSeriesSum(N);      return 0;  }

## Java

 // Java program for the above series  class GFG {             // Function to find the sum of series      static void printSeriesSum(int N)      {          double sum = 0;                 int a = 1;          int cnt = 0;                 // Flag to find the multiplicating          // factor.. i.e, by 2 or 3/2          boolean flag = true;                 // First term          sum += a;                 while (cnt < N) {                     int nextElement;                     // If flag is true, multiply by 2              if (flag == true) {                  nextElement = a * 2;                  sum += nextElement;                  flag = !flag;              }                     // If flag is false, multiply by 3/2              else {                  nextElement = a * 3 / 2;                  sum += nextElement;                  flag = !flag;              }                     // Update the previous element              // to nextElement              a = nextElement;              cnt++;          }                 // Print the sum          System.out.println(sum);      }             // Driver Code      public static void main (String[] args)      {                 int N = 8;                 printSeriesSum(N);      }  }  // This code is contributed by AnkitRai01

## Python3

 # Python3 program for the above series     # Function to find the sum of series  def printSeriesSum(N) :         sum = 0;         a = 1;      cnt = 0;         # Flag to find the multiplicating      # factor.. i.e, by 2 or 3/2      flag = True;         # First term      sum += a;         while (cnt < N) :             nextElement = None;             # If flag is true, multiply by 2          if (flag) :              nextElement = a * 2;              sum += nextElement;              flag = not flag;             # If flag is false, multiply by 3/2          else :              nextElement = a * (3 / 2);              sum += nextElement;              flag = not flag;             # Update the previous element          # to nextElement          a = nextElement;          cnt += 1        # Print the sum      print(sum);     # Driver Code  if __name__ == "__main__" :            N = 8;         printSeriesSum(N);             # This code is contributed by AnkitRai01

## C#

 // C# program for the above series  using System;     class GFG {              // Function to find the sum of series       static void printSeriesSum(int N)       {           double sum = 0;                  int a = 1;           int cnt = 0;                  // Flag to find the multiplicating           // factor.. i.e, by 2 or 3/2           bool flag = true;                  // First term           sum += a;                  while (cnt < N) {                      int nextElement;                      // If flag is true, multiply by 2               if (flag == true) {                   nextElement = a * 2;                   sum += nextElement;                   flag = !flag;               }                      // If flag is false, multiply by 3/2               else {                   nextElement = a * 3 / 2;                   sum += nextElement;                   flag = !flag;               }                      // Update the previous element               // to nextElement               a = nextElement;               cnt++;           }                  // Print the sum           Console.WriteLine(sum);       }              // Driver Code       public static void Main (string[] args)       {                  int N = 8;                  printSeriesSum(N);       }   }      // This code is contributed by AnkitRai01

Output:

201


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Improved By : AnkitRai01