Three numbers form a geometric sequence where T(3) = 12. If T(3) is changed to 9 , these three numbers form an arithmetic sequence. Find these numbers.
thanks~
maths sequence
2008-09-24 4:16 am
回答 (1)
2008-09-24 4:51 am
✔ 最佳答案
For geometric sequence:12 = T(2) x R
T(2) = T(1) x R
so, 12 = [T(2) ^ 2] / T(1)
For arithmetic sequence:
9 = T(2) + X
T(2) = T(1) + X
so, 9 = 2 x T(2) - T(1)
By substituting T(1),
[T(2) ^ 2] - 24 x T(2) + 108 = 0
by solving the above quadratic equation, we get
[T(2) - 6] x [T(2) - 18] = 0
As a result, T(1) = [T(2) ^ 2] / 12 = 3 and T(2) = 6
收錄日期: 2021-04-23 18:08:20
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080923000051KK01861