# Find the sum of the series 2, 5, 13, 35, 97…

• Last Updated : 19 Mar, 2021

Given a series and a number n, the task is to find the sum of its first n terms. Below is the series:

2, 5, 13, 35, 97, …

Examples:

Input: N = 2
Output: 7
The sum of first 2 terms of Series is
2 + 5 = 7

Input: N = 4
Output: 55
The sum of first 4 terms of Series is
2 + 5 + 13 + 35 = 55

Approach: From this given series we find it is the sum of the Two GP series with common ratioes 2, 3 .

Sn = 2 + 5 + 13 + 35 + 97 … + upto nth term
Sn = (2^0 + 3^ 0) + (2^1 + 3^1) + (2^2 + 3^2) + (2^3 + 3^3)+ (2^4 + 3^4) …… + upto nth term
Sn = (2^0 + 2^1 + 2^2 + 2^3 + 2^4 … + upto nth term) + ( 3^0 + 3^1 + 3^2 + 3^3 …… + unto nth term )

Since, We know that the sum of n terms of the GP is given by the following formula: Below is the implementation of the above approach:

## C++

 // C++ program for finding the sum// of first N terms of the series.#include using namespace std; // CalculateSum function returns the final sumint calculateSum(int n){    // r1 and r2 are common ratios    // of 1st and 2nd series    int r1 = 2, r2 = 3;     // a1 and a2 are common first terms    // of 1st and 2nd series    int a1 = 1, a2 = 1;     return a1 * (pow(r1, n) - 1) / (r1 - 1)           + a2 * (pow(r2, n) - 1) / (r2 - 1);} // Driver codeint main(){    int n = 4;     // function calling for 4 terms    cout << "Sum = " << calculateSum(n)         << endl;     return 0;}

## Java

 //Java program for finding the sum//of first N terms of the series. public class GFG {     //CalculateSum function returns the final sum    static int calculateSum(int n)    {     // r1 and r2 are common ratios     // of 1st and 2nd series     int r1 = 2, r2 = 3;      // a1 and a2 are common first terms     // of 1st and 2nd series     int a1 = 1, a2 = 1;      return (int)(a1 * (Math.pow(r1, n) - 1) / (r1 - 1)            + a2 * (Math.pow(r2, n) - 1) / (r2 - 1));    }     //Driver code    public static void main(String[] args) {                 int n = 4;          // function calling for 4 terms         System.out.println("Sum = " +calculateSum(n));    }}

## Python 3

 # Python 3 program for finding the sum# of first N terms of the series. # from math import everythingfrom math import * # CalculateSum function returns the final sumdef calculateSum(n) :     # r1 and r2 are common ratios    # of 1st and 2nd series    r1, r2 = 2, 3     # a1 and a2 are common first terms    # of 1st and 2nd series    a1, a2 = 1, 1     return (a1 * (pow(r1, n) - 1) // (r1 - 1)           + a2 * (pow(r2, n) - 1) // (r2 - 1)) # Driver Codeif __name__ == "__main__" :     n = 4     # function calling for 4 terms    print("SUM = ",calculateSum(n))  # This code is contributed by ANKITRAI1

## C#

 // C# program for finding the sum// of first N terms of the series.using System; class GFG{ // CalculateSum function// returns the final sumstatic int calculateSum(int n){// r1 and r2 are common ratios// of 1st and 2nd seriesint r1 = 2, r2 = 3; // a1 and a2 are common first// terms of 1st and 2nd seriesint a1 = 1, a2 = 1; return (int)(a1 * (Math.Pow(r1, n) - 1) / (r1 - 1) +             a2 * (Math.Pow(r2, n) - 1) / (r2 - 1));} // Driver codestatic public void Main (){    int n = 4;     // function calling for 4 terms    Console.Write("Sum = " +                   calculateSum(n));}} // This code is contributed by Raj

## PHP

 

## Javascript

 
Output:
Sum = 55

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