maths (f.1,急)(3題only!!!)

(a).3分2,9分2,27分2,81分2
general term=2/3^n

(b).2,6,18,54
general term=2*[3^(n-1)]

(c).3,4分3,16分3,64分3
general term=3/[4^(n-1)]

2007-12-14 00:34:18 補充：
where n is the number of the term

(a)
n=1 T(1) = 2/3= 2(1/3)
n=2 T(2) = 2(1/3)(1/3) =2(1/3)^2
n=3 T(3) = 2(1/3)(1/3)(1/3) = 2(1/3)^3
n=4 T(4) = 2(1/3)(1/3)(1/3)(1/3) = 2(1/3)^4
Therefore general term = 2(1/3)^n

(b)
n=1 T(1) = 2 = 2(3)^(1-1)
n=2 T(2) = 2 x 3 = 2(3)^(2-1)
n=3 T(3) = 2 x 3 x 3 = 2(3)^(3-1)
n=4 T(4) = 2 x 3 x 3 x 3 = 2(3)^(4-1)
Therefore general term = 2(3)^(n-1)

(c)
n=1 T(1) = 3 = 3(1/4)^(1-1)
n=2 T(2) = 3 x (1/4) = 3(1/4)^(2-1)
n=3 T(3) = 3 x (1/4) x (1/4) = 3(1/4)^(3-1)
n=4 T(4) = 3 x (1/4) x (1/4) x (1/4) = 3(1/4)^(4-1)
Therefore general term = 3(1/4)^(n-1)

(a) 2留意o既係分母~
3分2，3 的一次方
9 分2，3的二次方 = 3 x 3 = 9
27分2，3的三次方 = 3 x 3 x 3 = 27
81分2， 3的四次方 = 3 x 3 x 3 x3 = 81
所以下一個會是~~
243分1 ，3的五次方 = 3x3x3x3x3 = 243

(b) 2 ， 6 ，18 ，54
2
6= 2 x 3
18= 6 x3
54 = 18 x3
所以下一個是~
162= 54 x3

(c) 睇分母~~
3 ，其實就係 1分3
4分3 ，1 x 4
16分3 ，4 x 4
64分3 ，16 x 4
所以下一個是~~
192分3，64 x3 = 192

(a)前項乘3分1
(b)前項乘3
(c)前項乘4分1