Python 程序：計算等差數列和

寫一個 Python 程序，用一個實際例子求算術級數(A.P .級數)的和。

Python 自動編程系列

算術數列是一個術語序列，其中下一個項目是通過將一個共同的差異加到上一個項目上而獲得的。或者 A.P .級數是任意兩個連續數的差總是相同的一系列數。這種差異稱為共同差異。

在計算等差數列的數學中
數列的和:Sn = n/2(2a+(n–1)d)
數列的 Tn 項:Tn = a+(n–1)d

尋找等差數列和的 Python 程序示例

這個 Python 程序允許用戶輸入第一個值、一個系列中的項目總數以及共同的區別。接下來，Python 找到算術級數的和。

# Python Program to find Sum of Arithmetic Progression Series

a = int(input("Please Enter First Number of an A.P Series: : "))
n = int(input("Please Enter the Total Numbers in this A.P Series: : "))
d = int(input("Please Enter the Common Difference : "))

total = (n * (2 * a + (n - 1) * d)) / 2
tn = a + (n - 1) * d

print("\nThe Sum of Arithmetic Progression Series = " , total)
print("The tn Term of Arithmetic Progression Series = " , tn)

計算等差數列和的 Python 程序示例 2

這個 Python 的 A.P 程序的和同上。這裡我們用 While Loop 顯示 A.P 系列，可選。

# Python Program to find Sum of Arithmetic Progression Series

a = int(input("Please Enter First Number of an A.P Series: : "))
n = int(input("Please Enter the Total Numbers in this A.P Series: : "))
d = int(input("Please Enter the Common Difference : "))

total = (n * (2 * a + (n - 1) * d)) / 2
tn = a + (n - 1) * d
i = a
print("\nThe tn Term of Arithmetic Progression Series = " , tn)
print("The Sum of Arithmetic Progression Series : ")
while(i <= tn):
    if(i != tn):
        print("%d + " %i, end = " ")
    else:
        print("%d = %d" %(i, total))
    i = i + d

算術級數和輸出

Please Enter First Number of an A.P Series: : 2
Please Enter the Total Numbers in this A.P Series: : 6
Please Enter the Common Difference : 4

The tn Term of Arithmetic Progression Series =  22
The Sum of Arithmetic Progression Series : 
2 +  6 +  10 +  14 +  18 +  22 = 72

不用數學公式計算等差數列和的 Python 程序

在這個 Python 程序中，我們沒有使用任何數學公式。

# Python Program to find Sum of Arithmetic Progression Series

a = int(input("Please Enter First Number of an A.P Series: : "))
n = int(input("Please Enter the Total Numbers in this A.P Series: : "))
d = int(input("Please Enter the Common Difference : "))

total = 0
value = a
print("Arithmetic Progression Series : ", end = " ")
for i in range(n):
    print("%d + " %value, end = " ")
    total = total + value
    value = value + d

print("\nThe Sum of Arithmetic Progression Series upto %d = %d " %(n, total))

Python 算術級數求和輸出

Please Enter First Number of an A.P Series: : 1
Please Enter the Total Numbers in this A.P Series: : 4
Please Enter the Common Difference : 5
Arithmetic Progression Series :  1 +  6 +  11 +  16 +  
The Sum of Arithmetic Progression Series upto 4 = 34

用函數計算等差數列和的 Python 程序

這個 Python 算術級數和與第一個例子相同。但是，我們使用函數來分離邏輯。

# Python Program to find Sum of Arithmetic Progression Series

def sumofAP(a, n, d):
    total = (n * (2 * a + (n - 1) * d)) / 2
    return total

a = int(input("Please Enter First Number of an A.P Series: : "))
n = int(input("Please Enter the Total Numbers in this A.P Series: : "))
d = int(input("Please Enter the Common Difference : "))

total = sumofAP(a, n, d)
print("\nThe Sum of Arithmetic Progression Series = " , total)