Find the Nth term of the series 1 + 2 + 6 + 15 + 31 + 56 + …
Given an integer . The task is to write a program to find the N-th term of the given series:
1 + 2 + 6 + 15 + 31 + 56 + ...
Examples:
Input : N = 8
Output : 141
Input : N = 20
Output : 2471
Approach:
The given series is:
1, 2, 6, 15, 31, 56, 92, 141, ...
First consecutive difference:
1 4 9 16 25 36 49 .......
Second consecutive difference:
3 5 7 9 11 13......
As the second consecutive difference is in AP, the nth term (tn) of the series is of the form,
A(n – 1)(n – 2)(n – 3) + B(n – 1)(n – 2) + C(n – 1) + D
So, tn = A(n – 1)(n – 2)(n – 3) + B(n – 1)(n – 2) + C(n – 1) + D
Now,
t1 = D = 1
t2 = C (2 – 1) + D = 2
t3 = 2B + 2C + D = 6
t4 = CA + 6B + 3C + D = 15
On solving the above four equations we get => A = 1/3, B = 3/2, C = 1, D = 1. On substituting these values tn and after simplifying we get,
Below is the implementation of above approach:
C++
#include<iostream>
#include<math.h>
using namespace std;
int Nth_Term( int n)
{
return (2 * pow (n, 3) - 3 *
pow (n, 2) + n + 6) / 6;
}
int main()
{
int N = 8;
cout << Nth_Term(N);
}
|
Java
import java.util.*;
import java.lang.*;
class GFG
{
static double Nth_Term( int n)
{
return ( 2 * Math.pow(n, 3 ) - 3 *
Math.pow(n, 2 ) + n + 6 ) / 6 ;
}
static public void main (String args[])
{
int N = 8 ;
System.out.println(Nth_Term(N));
}
}
|
Python3
def Nth_Term(n):
return ( 2 * pow (n, 3 ) - 3 * pow (n, 2 ) + n + 6 ) / / 6
N = 8
print (Nth_Term(N))
|
C#
using System;
class GFG
{
static double Nth_Term( int n)
{
return (2 * Math.Pow(n, 3) - 3 *
Math.Pow(n, 2) + n + 6) / 6;
}
static public void Main ()
{
int N = 8;
Console.WriteLine(Nth_Term(N));
}
}
|
PHP
<?php
function Nth_Term( $n )
{
return (2 * pow( $n , 3) - 3 *
pow( $n , 2) + $n + 6) / 6;
}
$N = 8;
echo Nth_Term( $N );
?>
|
Javascript
<script>
function Nth_Term(n)
{
return (2 * Math.pow(n, 3) - 3 *
Math.pow(n, 2) + n + 6) / 6;
}
let N = 8;
document.write(Nth_Term(N));
</script>
|
Time Complexity: O(1), since there is no loop or recursion.
Auxiliary Space: O(1), since no extra space has been taken.
Last Updated :
11 Aug, 2022
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