會考數學問題(sequence)

[匿名]

2010-05-15 7:03 pm

1)if x>y>0, x is the second term of a geometric sequence and y is the third term of the sequence. find the sum to infinity of the sequence.
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2)the common difference of the arithmetic sequence s1,s2,s2,....Is given by d. find the general term of the arithmetic sequence 1-3s1, 1-3s2, 1-3s3,....
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3)a bag contains w green balls, x red balls, y blue balls and z black balls. Given that w:x=2:3, x:y=4:5,and y:z=6:7. a ball is drawn at random from the bag. find the probability of getting a green ball in term of z
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thz

回答 (1)

用戶2053

2010-05-15 8:04 pm

✔ 最佳答案

1) r = y/x ,
the 1st term = x / (y/x) = (x^2)/y
the sum to infinity of the sequence
= [(x^2)/y] / (1 - y/x)
= [(x^2)/y] / [(x - y)/x]
= (x^3) / [y(x - y)]
2) Common difference of the arithmetic sequence 1-3s1, 1-3s2, 1-3s3 ...
= (1-3s2) - (1-3s1) = 3s1 - 3s2 = 3(s1 - s2) = 3(-d) = -3d
the general term
T(n) = (1 - 3s1) + (-3d)(n-1)
T(n) = 1 - 3s1 - (3d)(n-1)
T(n) = 1 - 3(s1 + d(n-1))
3)
w:x=2:3, x:y=4:5,and y:z=6:7 ,
w : x = 8 : 12 , x : y = 12 : 15 , and y:z=6:7 ,
w : x : y = 8 : 12 : 15 , and y:z=6:7
w : x : y = 16 : 24 : 30 , and y : z = 30 : 35
w : x : y : z = 16 : 24 : 30 : 35
the probability of getting a green ball
= 16 / (16 + 24 + 30 + 35)
= 16/105
= 16/(3x35)
the probability of getting a green ball in term of z
= w / 3z
= (16/35)z / (3z)

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