程序找到级数3,7,13,21,31的第n项…..

2021年4月29日18:23:42 发表评论 1,343 次浏览

本文概述

给定数字N, 任务是找到该级数的第N个项:

3、7、13、21、31, ……。

例子:

Input: N = 4
Output: 21
Explanation:
Nth term = (pow(N, 2) + N + 1)
         = (pow(4, 2) + 4 + 1)
         = 21

Input: N = 11
Output: 133

方法:

总和= 0 + 3 + 7 + 13 + 21 + 31 + ........ + a_ {n-1} + a_n \\总和= 3 + 7 + 13 + 21 + 31 + ... + a_ {n-2} + a_ {n-1} + a_n

减去这两个方程, 我们得到

$ 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 $

因此, 给定级数的第N个项是:

下面是上述方法的实现:

C ++

//CPP program to find the Nth term of given series.
#include <iostream>
#include <math.h>
using namespace std;
  
//Function to calculate sum
long long int getNthTerm( long long int N)
{
     //Return Nth term
     return ( pow (N, 2) + N + 1);
}
  
//driver code
int main()
{
     //declaration of number of terms
     long long int N = 11;
  
     //Get the Nth term
     cout <<getNthTerm(N);
  
     return 0;
}

Java

//Java code to find the Nth term of given series.
import java.util.*;
  
class solution
{
  
//Function to calculate sum
static long getNthTerm( long N)
{
      
    //Return Nth term
     return (( int )Math.pow(N, 2 ) + N + 1 );
}
  
//Driver program
public static void main(String arr[])
{
      
    //declaration of number of terms
     long N = 11 ;
  
     //Get the Nth term
     System.out.println(getNthTerm(N));
  
}
}
//THis code is contibuted by
//Surendra_Gangwar

Python3

# Python3 Code to find the
# Nth term of given series.
  
# Function to calculate sum
def getNthTerm(N):
      
     # Return Nth term
     return ( pow (N, 2 ) + N + 1 )
  
# driver code
if __name__ = = '__main__' :
      
# declaration of number of terms
     N = 11
      
# Get the Nth term
     print (getNthTerm(N))
  
# This code is contributed by
# Sanjit_Prasad

C#

//C# code to find the Nth
//term of given series.
using System;
  
class GFG
{
  
//Function to calculate sum
static long getNthTerm( long N)
{
      
//Return Nth term
     return (( int )Math.Pow(N, 2) + N + 1);
}
  
//Driver Code
static public void Main ()
{
      
     //declaration of number
     //of terms
     long N = 11;
  
     //Get the Nth term
     Console.Write(getNthTerm(N));
}
}
  
//This code is contibuted by Raj

的PHP

<?php
//PHP program to find the 
//Nth term of given series 
  
//Function to calculate sum 
function getNthTerm( $N ) 
{ 
     //Return Nth term 
     return (pow( $N , 2) + $N + 1); 
} 
  
//Driver code 
  
//declaration of number of terms 
$N = 11; 
  
//Get the Nth term 
echo getNthTerm( $N ); 
  
//This code is contributed by Raj
?>

输出如下:

133

时间复杂度:O(1)


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