Question

在15,25之间插入3个数,使这五个数构成等差数列,求这三个数

Answer 1

25 - 15 = 10
等差 = 10/4 = 2.5
第一个数 = 15 + 2.5 = 17.5
第二个数 = 17.5 + 2.5 = 20
第三个数 = 20 + 2.5 = 22.5

用联立方程也可以：
设这三个数分别为a，b，c
15 - a = a - b
2a - b = 15 ...(1)

a - b = b - c
2b = a + c ...(2)

b - c = c - 25
2c = b + 25 ...(3)

联立(1)(2)消去b
2(2a - b) + 2b = 2(15) + a + c
4a = 30 + a + c
3a - c = 30 ...(4)

联立(2)(3)消去b
2b + 2(2c) = a + c + 2(b + 25)
4c = a + c + 50
3c - a = 50 ...(5)

联立(4)(5)消去c
3(3a - c) + 3c - a = 3(30) + 50
8a = 140
a = 17.5

b = 2a - 15 = 2(17.5) - 15 = 20

c = 3a - 30 = 22.2

所以这三个数分别是17.5，20，22.5