1 3 7 13 21
Plan to find the Nth term of the series 3, vii, 13, 21, 31…..
Given a number Due north, the task is to notice the Nth term of this serial:
3, seven, thirteen, 21, 31, …….
Examples:
Input: N = iv Output: 21 Explanation: Nth term = (pow(N, 2) + N + i) = (pow(4, 2) + 4 + 1) = 21 Input: Northward = 11 Output: 133
Approach:
Subtracting these two equations we get
![0=3+\left \{\frac{n-1}{2}\right \}[2*4 + (n-2)*2]-a_n\\ =3+\left \{\frac{n-1}{2}\right \}[8 + 2n-4]-a_n\\ =3+\left \{\frac{n-1}{2}\right \}[2n+4]-a_n\\ a_n=3+(n-1)(n+2)\\ a_n=n^2+n+1](https://www.geeksforgeeks.org/wp-content/ql-cache/quicklatex.com-1acdb3e613abd7083f3f1b7060d95192_l3.png "Rendered by QuickLaTeX.com")
Therefore, the Nth Term of the given series is:
Below is the implementation of the to a higher place approach:
C++
#include <iostream>
#include <math.h>
using namespace std;
long long int getNthTerm( long long int North)
{
return ( pow (N, 2) + N + 1);
}
int main()
{
long long int N = 11;
cout << getNthTerm(North);
return 0;
}
Java
import java.util.*;
class solution
{
static long getNthTerm( long N)
{
return (( int )Math.pow(N, two ) + N + 1 );
}
public static void primary(String arr[])
{
long North = 11 ;
System.out.println(getNthTerm(N));
}
}
Python3
def getNthTerm(N):
return ( pw (N, 2 ) + N + i )
if __name__ = = '__main__' :
Due north = eleven
print (getNthTerm(N))
C#
using System;
class GFG
{
static long getNthTerm( long N)
{
return (( int )Math.Pow(N, ii) + N + 1);
}
static public void Main ()
{
long N = 11;
Console.Write(getNthTerm(North));
}
}
PHP
<?php
function getNthTerm( $N )
{
render (pow( $Northward , 2) + $Due north + 1);
}
$Due north = eleven;
echo getNthTerm( $North );
?>
Javascript
<script>
function getNthTerm(North)
{
return (Math.pow(North, two) + Due north + 1);
}
let N = 11;
document.write(getNthTerm(N));
</script>
Time Complexity: O(1)
Space Complexity: O(1) since using constant variables
1 3 7 13 21,
Source: https://www.geeksforgeeks.org/program-to-find-the-nth-term-of-the-series-3-7-13-21-31/
Posted by: shawpuble1956.blogspot.com
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