超簡單的數學題6! 請教教我

1.求下列各等比數列的項數ｎ和首ｎ項之和S(n)。

(a) 1458 ,486 ,162 ,54 ,...,2
a = 1458
r = 486/1458 = 1/3
T(n) = 1458 (1/3)^(n-1) = 2
(1/3)^(n-1) = 1/729
(1/3)^(n-1) = (1/3)^6
n = 7
S(7)
= (1458) [ 1 - (1/3)^7 ] / [ 1 - (1/3) ]
= 2186

(b) 1536 , -768, 384, -192,...,-3
r = -768/1536 = -1/2
T(n) = (1536) (-1/2)^(n-1) = -3
(-1/2)^(n-1) = -1/512
(-1/2)^(n-1) = (-1/2)^9
n = 10
S(10)
= (1536) [ 1 - (-1/2)^10 ] / [ 1 - (-1/2) ]
= 1023

(c) 2, -8 , 32 , -128 , -128 ,...,-2048
反正都一樣做法, 自己諗下做下, 唔好咁懶
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2. 某等比數列的首項是１／３，第４項是－１／８１。

(a) 求該數列的公比。
(1/3)r^3 = -1/81
r^3 = -1/27
r^3 = (-1/3)^3
r = -1/3

(b)　由此，求首６項之和
(1/3) [ 1 - (-1/3)^6 ] / [ 1 - (-1/3) ]
= (1/3) [ 1 - 1/729 ] / [ 4/3 ]
= (1/3) [ 728/729 ] / [ 4/3 ]
= 182/729
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３．已知ｘ＋２、１３－ｘ和１７＋ｘ是某等比數列的首３項。

(a) 求x的值。
(13 - x) / (x + 2) = (17 + x) / (13 - x)
(13 - x)^2 = (17 + x)(x + 2)
169 - 26x + x^2 = x^2 + 19x + 34
45x = 135
x = 3

(b) 求首10項之和。
等比數列 : 5, 10, 20 ....
a = 5, r = 2
S(10)
= (5)(2^10 - 1)/(2 - 1)
= 5115
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4. 某等比數列的公比是2/3，第n項是16，首n項之和是211。

(a) 求該數列的首項。
T(n) = a (2/3)^(n-1) = 16 --------- (1)
S(n) = a [ 1 - (2/3)^n ] / [ 1 - (2/3) ] = 211
a [ 1 - (2/3)^n ] / [ 1/3 ] = 211
3a [ 1 - (2/3)^n ] = 211
3a - 3a (2/3)^n = 211
3a - 3 (2/3)(16) = 211, from (1)
a = 81

(b) 求n的值。
(81) (2/3)^(n-1) = 16
(2/3)^(n-1) = 16/81
(2/3)^(n-1) = (2/3)^4
n-1 = 4
n = 5

你講到咁簡單.....你就自已做la! = =