我们给定了整数n,在接下来的行中还有2 * n个整数,它们表示算术级数序列a 1 ,a 2 ,a 3 …a 2n,它们位于AP中。我们需要找到1 2 – a 2 2 + a 3 2 …的总和。 + a 2n-1 2 – a 2n 2 。
例子 :
Input : n = 2
a[] = {1 2 3 4}
Output : -10
Explanation : 12 - 22 +
32 42 = -10.
Input : n = 3
a[] = {2 4 6 8 10 12}
Output : -84
简单方法:我们逐一找出偶数项为负,奇数为正项的平方和。
C++
// CPP program to find sum of
// series with alternate signed
// square AP sums.
#include
using namespace std;
// function to calculate series sum
int seiresSum(int n, int a[])
{
int res = 0;
for (int i = 0; i < 2 * n; i++)
{
if (i % 2 == 0)
res += a[i] * a[i];
else
res -= a[i] * a[i];
}
return res;
}
// Driver Code
int main()
{
int n = 2;
int a[] = { 1, 2, 3, 4 };
cout << seiresSum(n, a);
return 0;
}
Java
// Java program to find sum of
// series with alternate signed
// square AP sums.
import java.io.*;
import java.lang.*;
import java.util.*;
class GFG
{
// function to calculate
// series sum
static int seiresSum(int n,
int[] a)
{
int res = 0, i;
for (i = 0; i < 2 * n; i++)
{
if (i % 2 == 0)
res += a[i] * a[i];
else
res -= a[i] * a[i];
}
return res;
}
// Driver code
public static void main(String args[])
{
int n = 2;
int a[] = { 1, 2, 3, 4 };
System.out.println(seiresSum(n, a));
}
}
Python3
# Python3 program to find sum
# of series with alternate signed
# square AP sums.
# Function to calculate series sum
def seiresSum(n, a):
res = 0
for i in range(0, 2 * n):
if (i % 2 == 0):
res += a[i] * a[i]
else:
res -= a[i] * a[i]
return res
# Driver code
n = 2
a = [1, 2, 3, 4]
print(seiresSum(n, a))
# This code is contributed by Ajit.
C#
// C# program to find sum of
// series with alternate signed
// square AP sums.
using System;
class GFG
{
// function to calculate
// series sum
static int seiresSum(int n,
int[] a)
{
int res = 0, i;
for (i = 0; i < 2 * n; i++)
{
if (i % 2 == 0)
res += a[i] * a[i];
else
res -= a[i] * a[i];
}
return res;
}
// Driver code
public static void Main()
{
int n = 2;
int []a = { 1, 2, 3, 4 };
Console.WriteLine(seiresSum(n, a));
}
}
//This code is contributed by vt_m.
PHP
Javascript
C++
// Efficient CPP program to
// find sum of series with
// alternate signed square AP sums.
#include
using namespace std;
// function to calculate
// series sum
int seiresSum(int n, int a[])
{
return n * (a[0] * a[0] - a[2 * n - 1] *
a[2 * n - 1]) / (2 * n - 1);
}
// Driver code
int main()
{
int n = 2;
int a[] = { 1, 2, 3, 4 };
cout << seiresSum(n, a);
return 0;
}
Java
// Efficient Java program to
// find sum of series with
// alternate signed square AP sums.
import java.io.*;
import java.lang.*;
import java.util.*;
class GFG
{
static int seiresSum(int n,
int[] a)
{
return n * (a[0] * a[0] - a[2 * n - 1] *
a[2 * n - 1]) / (2 * n - 1);
}
// Driver Code
public static void main(String args[])
{
int n = 2;
int a[] = { 1, 2, 3, 4 };
System.out.println(seiresSum(n, a));
}
}
Python3
# Efficient Python3 program
# to find sum of series with
# alternate signed square AP sums.
# Function to calculate
# series sum
def seiresSum(n, a):
return (n * (a[0] * a[0] - a[2 * n - 1] *
a[2 * n - 1]) / (2 * n - 1))
# Driver code
n = 2
a = [1, 2, 3, 4]
print(int(seiresSum(n, a)))
# This code is contributed
# by Smitha Dinesh Semwal.
C#
// Efficient C# program to find sum
// of series with alternate signed
// square AP sums.
using System;
class GFG
{
static int seiresSum(int n, int[] a)
{
return n * (a[0] * a[0] - a[2 * n - 1] *
a[2 * n - 1]) / (2 * n - 1);
}
// Driver Code
public static void Main()
{
int n = 2;
int []a= { 1, 2, 3, 4 };
Console.WriteLine(seiresSum(n, a));
}
}
// This code is contributed by anuj_67..
PHP
Javascript
输出 :
-10
高效方法:使用算术级数应用
我们知道共同差d = a 2 – a 1 = a 3 – a 2 = a 4 – a 3
结果= a 1 2 – a 2 2 + a 3 2 …。 + 2n-1 2 – 2n 2
=(a 1 – a 2 )*(a 1 + a 2 )+(a 3 – a 4 )*(a 3 + a 4 )+…。+(a 2n-1 – a 2n )*(a 2n- 1 + a 2n )
因此,由于该系列共有相同之处,因此:
(a 1 – a 2 )[a 1 + a 2 + a 3 …a 2n ]
现在我们可以写:
(-d)*(Sum of the term of the 2n term of AP)
(-d)*[((2*n)*(a1 + a2n))/2]
now we know that common difference is : d = (a1 - a2)
Then the difference between : g = (a2n - a1)
So we can conclude that g = d*(2*n - 1)
the we ca replace d by : g/(2*n - 1)
So our result becomes : (n/(2*n - 1)) * (a12 - a2n2)
C++
// Efficient CPP program to
// find sum of series with
// alternate signed square AP sums.
#include
using namespace std;
// function to calculate
// series sum
int seiresSum(int n, int a[])
{
return n * (a[0] * a[0] - a[2 * n - 1] *
a[2 * n - 1]) / (2 * n - 1);
}
// Driver code
int main()
{
int n = 2;
int a[] = { 1, 2, 3, 4 };
cout << seiresSum(n, a);
return 0;
}
Java
// Efficient Java program to
// find sum of series with
// alternate signed square AP sums.
import java.io.*;
import java.lang.*;
import java.util.*;
class GFG
{
static int seiresSum(int n,
int[] a)
{
return n * (a[0] * a[0] - a[2 * n - 1] *
a[2 * n - 1]) / (2 * n - 1);
}
// Driver Code
public static void main(String args[])
{
int n = 2;
int a[] = { 1, 2, 3, 4 };
System.out.println(seiresSum(n, a));
}
}
Python3
# Efficient Python3 program
# to find sum of series with
# alternate signed square AP sums.
# Function to calculate
# series sum
def seiresSum(n, a):
return (n * (a[0] * a[0] - a[2 * n - 1] *
a[2 * n - 1]) / (2 * n - 1))
# Driver code
n = 2
a = [1, 2, 3, 4]
print(int(seiresSum(n, a)))
# This code is contributed
# by Smitha Dinesh Semwal.
C#
// Efficient C# program to find sum
// of series with alternate signed
// square AP sums.
using System;
class GFG
{
static int seiresSum(int n, int[] a)
{
return n * (a[0] * a[0] - a[2 * n - 1] *
a[2 * n - 1]) / (2 * n - 1);
}
// Driver Code
public static void Main()
{
int n = 2;
int []a= { 1, 2, 3, 4 };
Console.WriteLine(seiresSum(n, a));
}
}
// This code is contributed by anuj_67..
的PHP
Java脚本
输出 :
-10