算术级数求和程序-yiteyi-C++库

具有相同共同差异的序列称为 算术级数 .系列的第一项是 A. 两者的共同点是 D .这个系列看起来像 a、 a+d、a+2d、a+3d。 任务是求级数的和。例如：

null

Input : a = 1        d = 2        n = 4Output : 161 + 3 + 5 + 7 = 16Input : a = 2.5        d = 1.5        n = 20Output : 335

建议：请在“上解决” 实践 “首先，在讨论解决方案之前。

A. 简单解决方案 求算术级数之和。

C++

                         // CPP Program to find the sum of arithmetic                       
                         // series.                       
                         #include<bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         // Function to find sum of series.                       
                         float                                     sumOfAP(                                     float                                     a,                                     float                                     d,                                     int                                     n)                       
                         {                       
                                                 float                                     sum = 0;                       
                                                 for                                     (                                     int                                     i=0;i<n;i++)                       
                                                 {                       
                                                 sum = sum + a;                       
                                                 a = a + d;                       
                                                 }                       
                                                 return                                     sum;                       
                         }                       
           
                         // Driver function                       
                         int                                     main()                       
                         {                       
                                                 int                                     n = 20;                       
                                                 float                                     a = 2.5, d = 1.5;                       
                                                 cout<<sumOfAP(a, d, n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // JAVA Program to find the sum of                       
                         // arithmetic series.                       
           
                         class                                     GFG{                       
                                   
                                                 // Function to find sum of series.                       
                                                 static                                     float                                     sumOfAP(                                     float                                     a,                                     float                                     d,                       
                                                 int                                     n)                       
                                                 {                       
                                                 float                                     sum =                                     0                                     ;                       
                                                 for                                     (                                     int                                     i =                                     0                                     ; i < n; i++)                       
                                                 {                       
                                                 sum = sum + a;                       
                                                 a = a + d;                       
                                                 }                       
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver function                       
                                                 public                                     static                                     void                                     main(String args[])                       
                                                 {                       
                                                 int                                     n =                                     20                                     ;                       
                                                 float                                     a =                                     2                                     .5f, d =                                     1                                     .5f;                       
                                                 System.out.println(sumOfAP(a, d, n));                       
                                                 }                       
                         }                       
           
                         /*This code is contributed by Nikita Tiwari.*/                       

python

                         # Python Program to find the sum of                       
                         # arithmetic series.                       
           
                         # Function to find sum of series.                       
                         def                                     sumOfAP( a, d,n) :                       
                                                 sum                                     =                                     0                       
                                                 i                                     =                                     0                       
                                                 while                                     i < n :                       
                                                 sum                                     =                                     sum                                     +                                     a                       
                                                 a                                     =                                     a                                     +                                     d                       
                                                 i                                     =                                     i                                     +                                     1                       
                                                 return                                     sum                       
                                   
                         # Driver function                       
                         n                                     =                                     20                       
                         a                                     =                                     2.5                       
                         d                                     =                                     1.5                       
                         print                                     (sumOfAP(a, d, n))                       
           
                         # This code is contributed by Nikita Tiwari.                       

C#

                         // C# Program to find the sum of                       
                         // arithmetic series.                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 // Function to find sum of series.                       
                                                 static                                     float                                     sumOfAP(                                     float                                     a,                                     float                                     d,                       
                                                 int                                     n)                       
                                                 {                       
                                                 float                                     sum = 0;                       
                                                 for                                     (                                     int                                     i = 0; i < n; i++)                       
                                                 {                       
                                                 sum = sum + a;                       
                                                 a = a + d;                       
                                                 }                       
                                   
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver function                       
                                                 public                                     static                                     void                                     Main()                       
                                                 {                       
                                                 int                                     n = 20;                       
                                                 float                                     a = 2.5f, d = 1.5f;                       
                                   
                                                 Console.Write(sumOfAP(a, d, n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by parashar.                       

PHP

                         <?php                       
                         // PHP Program to find the sum                       
                         // of arithmetic series.                       
           
                         // Function to find sum of series.                       
                         function                                     sumOfAP(                                     $a                                     ,                                     $d                                     ,                                     $n                                     )                       
                         {                       
                                                 $sum                                     = 0;                       
                                                 for                                     (                                     $i                                     = 0;                                     $i                                     <                                     $n                                     ;                                     $i                                     ++)                       
                                                 {                       
                                                 $sum                                     =                                     $sum                                     +                                     $a                                     ;                       
                                                 $a                                     =                                     $a                                     +                                     $d                                     ;                       
                                                 }                       
                                                 return                                     $sum                                     ;                       
                         }                       
           
                         // Driver Code                       
                         $n                                     = 20;                       
                         $a                                     = 2.5;                                     $d                                     = 1.5;                       
                         echo                                     (sumOfAP(                                     $a                                     ,                                     $d                                     ,                                     $n                                     ));                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         <script>                       
           
                         // Javascript Program to find the sum of arithmetic                       
                         // series.                       
           
                         // Function to find sum of series.                       
                         function                                     sumOfAP(a, d, n)                       
                         {                       
                                                 let sum = 0;                       
                                                 for                                     (let i=0;i<n;i++)                       
                                                 {                       
                                                 sum = sum + a;                       
                                                 a = a + d;                       
                                                 }                       
                                                 return                                     sum;                       
                         }                       
           
                         // Driver function                       
           
                                                 let n = 20;                       
                                                 let a = 2.5, d = 1.5;                       
                                                 document.write(sumOfAP(a, d, n));                       
           
                                   
                         // This code is contributed by Mayank Tyagi                       
           
                         </script>                       

输出：

时间复杂度：O（n）一 有效解决方案 求算术级数之和要用到下面的公式。

Sum of arithmetic series            = ((n / 2) * (2 * a + (n - 1) * d))           Where               a - First term               d - Common difference               n - No of terms

C++

                         // Efficient solution to find sum of arithmetic series.                       
                         #include<bits/stdc++.h>                       
                         using                                     namespace                                     std;                       
           
                         float                                     sumOfAP(                                     float                                     a,                                     float                                     d,                                     float                                     n)                       
                         {                       
                                                 float                                     sum = (n / 2) * (2 * a + (n - 1) * d);                       
                                                 return                                     sum;                       
                         }                       
           
                         // Driver code                       
                         int                                     main()                       
                         {                       
                                                 float                                     n = 20;                       
                                                 float                                     a = 2.5, d = 1.5;                       
                                                 cout<<sumOfAP(a, d, n);                       
                                                 return                                     0;                       
                         }                       

JAVA

                         // Java Efficient solution to find                       
                         // sum of arithmetic series.                       
                         class                                     GFG                       
                         {                       
                                                 static                                     float                                     sumOfAP(                                     float                                     a,                                     float                                     d,                                     float                                     n)                       
                                                 {                       
                                                 float                                     sum = (n /                                     2                                     ) * (                                     2                                     * a + (n -                                     1                                     ) * d);                       
                                                 return                                     sum;                       
                                                 }                       
           
                                                 // Driver code                       
                                                 public                                     static                                     void                                     main (String[] args)                       
                                                 {                       
                                                 float                                     n =                                     20                                     ;                       
                                                 float                                     a =                                     2                                     .5f, d =                                     1                                     .5f;                       
                                                 System.out.print(sumOfAP(a, d, n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Anant Agarwal.                       

Python3

                         # Python3 Efficient                       
                         # solution to find sum                       
                         # of arithmetic series.                       
           
                         def                                     sumOfAP(a,  d,  n):                       
                                                 sum                                     =                                     (n                                     /                                     2                                     )                                     *                                     (                                     2                                     *                                     a                                     +                                     (n                                     -                                     1                                     )                                     *                                     d)                       
                                                 return                                     sum                       
                                   
                         # Driver code                       
                         n                                     =                                     20                       
                         a                                     =                                     2.5                       
                         d                                     =                                     1.5                       
           
                         print                                     (sumOfAP(a, d, n))                       
           
                         # This code is                       
                         # contributed by sunnysingh                       
                                   

C#

                         // C# efficient solution to find                       
                         // sum of arithmetic series.                       
                         using                                     System;                       
           
                         class                                     GFG {                       
                                   
                                                 static                                     float                                     sumOfAP(                                     float                                     a,                       
                                                 float                                     d,                       
                                                 float                                     n)                       
                                                 {                       
                                                 float                                     sum = (n / 2) *                       
                                                 (2 * a +                       
                                                 (n - 1) * d);                       
                                                 return                                     sum;                       
                                                 }                       
                                   
                                                 // Driver code                       
                                                 static                                     public                                     void                                     Main ()                       
                                                 {                       
                                                 float                                     n = 20;                       
                                                 float                                     a = 2.5f, d = 1.5f;                       
                                                 Console.WriteLine(sumOfAP(a, d, n));                       
                                                 }                       
                         }                       
           
                         // This code is contributed by Ajit.                       

PHP

                         <?php                       
                         // Efficient PHP code to find sum                       
                         // of arithmetic series.                       
           
                         // Function to find sum of series.                       
                         function                                     sumOfAP(                                     $a                                     ,                                     $d                                     ,                                     $n                                     )                       
                         {                       
                                                 $sum                                     = (                                     $n                                     / 2) * (2 *                                     $a                                     +                       
                                                 (                                     $n                                     - 1) *                                     $d                                     );                       
                                                 return                                     $sum                                     ;                       
                         }                       
           
                         // Driver code                       
                         $n                                     = 20;                       
                         $a                                     = 2.5;                                     $d                                     = 1.5;                       
                         echo                                     (sumOfAP(                                     $a                                     ,                                     $d                                     ,                                     $n                                     ));                       
           
                         // This code is contributed by Ajit.                       
                         ?>                       

Javascript

                         // Efficient solution to find sum of arithmetic series.                       
           
                         function                                     sumOfAP(a, d, n) {                       
                                                 let sum = (n / 2) * (2 * a + (n - 1) * d);                       
                                                 return                                     sum;                       
                         }                       
           
                         // Driver code                       
                         let n = 20;                       
                         let a = 2.5, d = 1.5;                       
                         document.write(sumOfAP(a, d, n));                       
           
                         // This code is contributed by Ashok                       

输出

时间复杂度：O（1） 这个公式是如何工作的？ 我们可以用数学归纳法来证明这个公式。我们可以很容易地看到，这个公式适用于n=1和n=2。对于n=k-1，这是真的。

Let the formula be true for n = k-1.Sum of first k - 1 elements of geometric series is        = (((k-1))/ 2) * (2 * a + (k - 2) * d))We know k-th term of arithmetic series is        = a + (k - 1)*dSum of first k elements =       = Sum of (k-1) numbers + k-th element      = (((k-1)/2)*(2*a + (k-2)*d)) + (a + (k-1)*d)      = [((k-1)(2a + (k-2)d) + (2a + 2kd - 2d)]/2      = ((k / 2) * (2 * a + (k - 1) * d))

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