在5与121/8之间插入两个数,使前三个数成等差数列,后三个数成等比数列,求这两个数
1个回答

假设5,X,Y,121/8

5 + Y = 2X (等差数列)

121X/8 = Y * Y (等比数列)

X = 8Y^2 / 121

16Y^2 / 121 - Y - 5 = 0

(4Y/ 11)^2 - Y + (11/8)^2 - (11/8)^2 - 5 = 0

(4Y/11 - 11/8)^2 = (121 + 320) / 64 = 441/64

4Y/11 - 11/8 = ±21/8

4Y/11 = 11/8 ± 21/8

因为 5 < Y < 121/8

Y = 11

X = 8

=> 5, 8, 11, 121/8

10,7,4,1,-2 => 10 - 3 * (n-1)

-6,12,-24,48,-96 => -6 * (-2)^n

3,8,13,18,23 => 3 + 5 * (n-1)