Arithmetic and Geometric Sequence (2)

For geometric sequence, T(3) = ar^2 = 12...............(1)
For arithmetic sequence , T(3) = a + 2d = 9..............(2)
For G.S., T(2) = ar, for A.S., T(2) = a + d, therefore, ar = a + d..............(3)
From (2) a = 9 - 2d. Sub. into (3) we get
r = (9 -2d +d)/(9 -2d) = (9-d)/(9 -2d). Sub. into (1), we get
(9 - 2d)(9-d)^2/(9 - 2d)^2 = 12
(9-d)^2 = 12(9 -2d)
81 + d^2 - 18d = 108 - 24d
d^2 + 6d - 27 = 0
d = 3 and -9.
When d = 3, a = 3 and r = 2.
When d = -9, a = 3 and r = sqrt(12/27).
So the 3 numbers are:
1) 3,6, and 9 for A.S. and 3, 6, 12 for G.S.
2) 27, 18, 9 for A.S. and 27, 18 ,12 for G.S.

2008-09-13 13:24:07 補充：
Correction: When d = -9, a = 27, not 3. Sorry.