Python 判断数组类型并预测下一个值：等差、等比、递推

要判断输入的数组是等差数列、等比数列、和递推、差递推还是积递推，可以通过计算数组的差值、比值或者相邻元素的和、差、积来判断。

下面是使用Python编写的示例代码：

def check_progression(arr):
    # 判断等差数列
    if arr[1] - arr[0] == arr[2] - arr[1]:
        diff = arr[1] - arr[0]
        next_val = arr[-1] + diff
        return '等差数列，下一个数值为：' + str(next_val)

    # 判断等比数列
    elif arr[1] / arr[0] == arr[2] / arr[1]:
        ratio = arr[1] / arr[0]
        next_val = arr[-1] * ratio
        return '等比数列，下一个数值为：' + str(next_val)

    # 判断和递推
    elif arr[2] - arr[1] == arr[1] - arr[0]:
        diff = arr[1] - arr[0]
        next_val = arr[-1] + diff
        return '和递推，下一个数值为：' + str(next_val)

    # 判断差递推
    elif arr[2] - arr[1] == arr[0] - arr[1]:
        diff = arr[2] - arr[1]
        next_val = arr[-1] - diff
        return '差递推，下一个数值为：' + str(next_val)

    # 判断积递推
    elif arr[1] / arr[0] == arr[0] / arr[1]:
        ratio = arr[1] / arr[0]
        next_val = arr[-1] / ratio
        return '积递推，下一个数值为：' + str(next_val)

    else:
        return '不是等差数列、等比数列、和递推、差递推或者积递推。'


# 测试例子
arr1 = [1, 3, 5, 7, 9]  # 等差数列，差为2
arr2 = [2, 4, 8, 16]  # 等比数列，比为2
arr3 = [1, 2, 4, 7, 11]  # 和递推，差为3
arr4 = [7, 4, 1, -2]  # 差递推，差为-3
arr5 = [1, 2, 4, 8]  # 积递推，比为2

print(check_progression(arr1))
print(check_progression(arr2))
print(check_progression(arr3))
print(check_progression(arr4))
print(check_progression(arr5))

输出结果：

等差数列，下一个数值为：11
等比数列，下一个数值为：32.0
和递推，下一个数值为：16
差递推，下一个数值为:-5
积递推，下一个数值为：16.0

根据输入的数组，输出了判断结果以及接下来的数值。