Given a number n then Find the Average of first n even natural numbers
Ex.= 2 + 4 + 6 + 8 + 10 + 12 +………+ 2n.
Examples :
Input : 7 Output : 8 (2 + 4 + 6 + 8 + 10 + 12 + 14)/7 = 8 Input : 5 Output : 6 (2 + 4 + 6 + 8 + 10)/5 = 6
Naive Approach:- In this program iterate the loop , finding total sum of first n even numbers and divided by n.it take 0(N) time.
// C++ implementation to find Average // of sum of first n natural even numbers #include <bits/stdc++.h> using namespace std;
// function to find average of // sum of first n even numbers int avg_of_even_num( int n)
{ // sum of first n even numbers
int sum = 0;
for ( int i = 1; i <= n; i++)
sum += 2*i;
// calculating Average
return sum/n;
} // Driver Code int main()
{ int n = 9;
cout << avg_of_even_num(n);
return 0;
} |
// java implementation to find Average // of sum of first n natural even number import java.io.*;
class GFG {
// function to find average of
// sum of first n even numbers
static int avg_of_even_num( int n)
{
// sum of first n even numbers
int sum = 0 ;
for ( int i = 1 ; i <= n; i++)
sum += 2 *i;
// calculating Average
return (sum / n);
}
public static void main (String[] args) {
int n = 9 ;
System.out.print(avg_of_even_num(n));
}
} // this code is contributed by 'vt_m' |
# Python3 implementation to # find Average of sum of # first n natural even # number # Function to find average # of sum of first n even # numbers def avg_of_even_num(n):
# sum of first n even
# numbers
sum = 0
for i in range ( 1 , n + 1 ):
sum = sum + 2 * i
# calculating Average
return sum / n
n = 9
print (avg_of_even_num(n))
# This code is contributed by upendra singh bartwal |
// C# implementation to find // Average of sum of first // n natural even number using System;
class GFG {
// function to find average of
// sum of first n even numbers
static int avg_of_even_num( int n)
{
// sum of first n even numbers
int sum = 0;
for ( int i = 1; i <= n; i++)
sum += 2 * i;
// calculating Average
return (sum / n);
}
// driver code
public static void Main () {
int n = 9;
Console.Write(avg_of_even_num(n));
}
} // This code is contributed by 'vt_m' |
<?php // PHP implementation to find Average // of sum of first n natural even numbers // function to find average of // sum of first n even numbers function avg_of_even_num( $n )
{ // sum of first n even numbers
$sum = 0;
for ( $i = 1; $i <= $n ; $i ++)
$sum += 2 * $i ;
// calculating Average
return $sum / $n ;
} // Driver Code $n = 9;
echo (avg_of_even_num( $n ));
// This code is contributed by Ajit. ?> |
<script> // javascript implementation to find Average // of sum of first n natural even numbers // function to find average of // sum of first n even numbers function avg_of_even_num( n)
{ // sum of first n even numbers
let sum = 0;
for (let i = 1; i <= n; i++)
sum += 2*i;
// calculating Average
return sum/n;
} // Driver Code let n = 9;
document.write(avg_of_even_num(n));
// This code is contributed by todaysgaurav </script> |
Output :
10
Time Complexity : O(N)
Auxiliary Space: O(1) as it is using constant space
Method 2 :- The idea is the sum of first n even number is n(n+1), for find the Average of first n even numbers divide by n, hence formula is n(n + 1) / n = ( n + 1). i.e. Average of first n even numbers is n+1. it take 0(1) time.
Avg of sum of N even natural number = (N + 1)
Proof
Sum of first n terms of an A.P.(Arithmetic Progression) = (n/2) * [2*a + (n-1)*d].....(i) where, a is the first term of the series and d is the difference between the adjacent terms of the series. Here, a = 2, d = 2, applying these values to eq.(i), get Sum = (n/2) * [2*2 + (n-1)*2] = (n/2) * [4 + 2*n - 2] = (n/2) * (2*n + 2) = n * (n + 1) finding the Avg so divided by n = n*(n+1)/n = (n+1)
// CPP Program to find the average // of sum of first n even numbers #include <bits/stdc++.h> using namespace std;
// Return the average of sum // of first n even numbers int avg_of_even_num( int n)
{ return n+1;
} // Driver Code int main()
{ int n = 8;
cout << avg_of_even_num(n) << endl;
return 0;
} |
// Java Program to find the average // of sum of first n even numbers import java.io.*;
class GFG
{ // Return the average of sum
// of first n even numbers
static int avg_of_even_num( int n)
{
return n + 1 ;
}
public static void main (String[] args) {
int n = 8 ;
System.out.println(avg_of_even_num(n));
}
} // This code is contributed by vt_m |
# Python 3 Program to # find the average # of sum of first n # even numbers # Return the average of sum # of first n even numbers def avg_of_even_num(n) :
return n + 1
# Driven Program n = 8
print (avg_of_even_num(n))
# This code is contributed # by Nikita Tiwari. |
// C# Program to find the average // of sum of first n even numbers using System;
class GFG {
// Return the average of sum
// of first n even numbers
static int avg_of_even_num( int n)
{
return n + 1;
}
// driver code
public static void Main () {
int n = 8;
Console.Write(avg_of_even_num(n));
}
} // This code is contributed by vt_m |
<?php // PHP Program to find the average // of sum of first n even numbers // Return the average of sum // of first n even numbers function avg_of_even_num( $n )
{ return $n + 1;
} // Driver Code $n = 8;
echo (avg_of_even_num( $n ));
// This code is contributed by Ajit. ?> |
<script> // javascript Program to find the average // of sum of first n even numbers // Return the average of sum // of first n even numbers function avg_of_even_num(n)
{ return n + 1;
} var n = 8;
document.write(avg_of_even_num(n)); // This code is contributed by Amit Katiyar </script> |
Output:
9
Time Complexity: O(1)
Auxiliary Space: O(1)