The first three terms of a geometric sequence are respectively equel to the first,the third and the sixth terms of an arithmetric sequence .If the first term and common ratio of the geometric sequence are both greater than 1,which of the following must be true?
1.The common ratio of the geometric sequence is 3/2.
2.The first term of the arithmetric sequence is 4.
3.The common difference of the arithmetric sequence is 1.
geometric sequence?
2007-06-12 11:17 pm
回答 (1)
2007-06-13 12:15 am
✔ 最佳答案
The first one must be true.Let the 1st 3rd and 6th term of the AP be
X, X+2a, X+5a
(X+5a)/(X+2a) = (X+2a)/ (X)
5ax = 4ax + 4a^2
x=4a
Sub x=4a
common ratio = (X+2a)/ (X) = 6a / 4a = 3/2
There is no other condition to ensure that 2 and 3 is ture.
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