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

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:

     $$  S_n=\frac{a(r^n-1)}{(r-1)} $$


Below is the implementation of the above approach:

C++

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// C++ program for finding the sum
// of first N terms of the series.
#include <bits/stdc++.h>
using namespace std;
  
// CalculateSum function returns the final sum
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 a1 * (pow(r1, n) - 1) / (r1 - 1)
           + a2 * (pow(r2, n) - 1) / (r2 - 1);
}
  
// Driver code
int main()
{
    int n = 4;
  
    // function calling for 4 terms
    cout << "Sum = " << calculateSum(n)
         << endl;
  
    return 0;
}

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Java

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//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));
    }
}

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Python 3

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# Python 3 program for finding the sum 
# of first N terms of the series. 
  
# from math import everything
from math import *
  
# CalculateSum function returns the final sum 
def 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 Code
if __name__ == "__main__" :
  
    n = 4
  
    # function calling for 4 terms
    print("SUM = ",calculateSum(n))
  
  
# This code is contributed by ANKITRAI1

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C#

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// C# program for finding the sum
// of first N terms of the series.
using System;
  
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
static public void Main ()
{
    int n = 4;
  
    // function calling for 4 terms
    Console.Write("Sum = " +
                   calculateSum(n));
}
}
  
// This code is contributed by Raj

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PHP

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<?php
// PHP program for finding the sum 
// of first N terms of the series. 
  
// CalculateSum function returns 
// the final sum 
function calculateSum($n
    // r1 and r2 are common ratios 
    // of 1st and 2nd series 
    $r1 = 2;
    $r2 = 3; 
  
    // a1 and a2 are common first  
    // terms of 1st and 2nd series 
    $a1 = 1;
    $a2 = 1; 
  
    return $a1 * (pow($r1, $n) - 1) /
                     ($r1 - 1) + $a2 *
                 (pow($r2, $n) - 1) / 
                     ($r2 - 1); 
  
// Driver code 
$n = 4; 
  
// function calling for 4 terms 
echo "Sum = ", calculateSum($n); 
  
// This code is contributed by ash264
?>

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Output:

Sum = 55


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