Program to print the series 2, 15, 41, 80, 132, 197… till N terms

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Given a number N, the task is to print the first N terms of the following series:

2 15 41 80 132 197 275 366 470 587…

Examples:

Input: N = 7

Output: 2 15 41 80 132 197 275

Input: N = 3

Output: 2 15 41

Approach: From the given series we can find the formula for Nth term:

1st term = 2
2nd term = 15 = 13 * 1 + 2
3rd term = 41 = 13 * 2 + 15 = 13 * 3 + 2
4th term = 80 = 13 * 3 + 41 = 13 * 6 + 2
5th term = 132 = 13 * 4 + 80 = 13 * 10 + 2
.
.
Nth term = (13 * N * (N – 1)) / 2 + 2

Therefore:

Nth term of the series

$2, 15, 41, 80, 132, 197.... = 13 * (N * (N - 1)) / 2 + 2$

Then iterate over numbers in the range [1, N] to find all the terms using the above formula and print them.

Below is the implementation of above approach:

C++

// C++ implementation to print the 
// given with the given Nth term
 
#include "bits/stdc++.h"
using namespace std;
 
// Function to print the series
void printSeries(int N)
{
 
    int ith_term = 0;
 
    // Generate the ith term and
    for (int i = 1; i <= N; i++) {
 
        ith_term = (13 * i * (i - 1)) / 2 + 2;
        cout << ith_term << ", ";
    }
}
 
// Driver Code
int main()
{
    int N = 7;
 
    printSeries(N);
    return 0;
}

Java

// Java implementation to print the 
// given with the given Nth term
import java.util.*;
 
class GFG{
 
// Function to print the series
static void printSeries(int N)
{
    int ith_term = 0;
     
    // Generate the ith term and
    for(int i = 1; i <= N; i++)
    {
       ith_term = (13 * i * (i - 1)) / 2 + 2;
       System.out.print(ith_term + ", ");
    }
}
 
// Driver Code
public static void main(String[] args)
{
    int N = 7;
 
    printSeries(N);
}
}
 
// This code is contributed by Rajput-Ji

Python3

# Python3 implementation to print the
# given with the given Nth term
 
# Function to print the series
def printSeries(N):
     
    ith_term = 0;
 
    # Generate the ith term and
    for i in range(1, N + 1):
        ith_term = (13 * i * (i - 1)) / 2 + 2;
        print(int(ith_term), ", ", end = "");
 
# Driver Code
if __name__ == '__main__':
     
    N = 7;
     
    printSeries(N);
     
# This code is contributed by amal kumar choubey

C#

// C# implementation to print the 
// given with the given Nth term
using System;
 
class GFG{
 
// Function to print the series
static void printSeries(int N)
{
    int ith_term = 0;
     
    // Generate the ith term and
    for(int i = 1; i <= N; i++)
    {
       ith_term = (13 * i * (i - 1)) / 2 + 2;
       Console.Write(ith_term + ", ");
    }
}
 
// Driver Code
public static void Main(String[] args)
{
    int N = 7;
 
    printSeries(N);
}
}
 
// This code is contributed by Rajput-Ji

Javascript

<script>
// javascript implementation to print the 
// given with the given Nth term
 
 
// Function to print the series
function printSeries( N)
{
 
    let ith_term = 0;
 
    // Generate the ith term and
    for (let i = 1; i <= N; i++)
    {
        ith_term = (13 * i * (i - 1)) / 2 + 2;
       document.write( ith_term + ", ");
    }
}
 
// Driver Code
    let N = 7;
    printSeries(N);
     
    // This code is contributed by gauravrajput1
 
</script>

Output:

2, 15, 41, 80, 132, 197, 275,

Time complexity: O(n) because using a for loop

Auxiliary Space: O(1)

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