maths~~~~~

2010-04-05 8:46 am
設p、q及r為正值常數。若p=2q=4r,則下列何者必為等差數列?
I. p/4 ,q , 3r
II. p,q,r
III. logr,logq,lop
更新1:

I.p/4 ,q , 3r

回答 (1)

2010-04-05 9:10 am
✔ 最佳答案
(3r - q) - (q - p/4)
= 3r - 2q + p/4
= 3p/4 - p + p/4
= 0
so, (3r - q) = (q - p/4)
p/4 ,q , 3r forms A.P.

-------------------------------------------
(r - q) - (q - p)
= r - 2q + p
= p/4 - p + p
= p/4
not equal to zero
p,q,r cannot form A.P.
-------------------------------------------
(log p - log q) - (log q - log r)
= log p - 2log q + log r
= log pr/q^2
= log 4pr / (2q)^2
= log p^2 / p^2
= log 1
= 0
so A.P.
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