數列 急問~~

a) 1/5+( -2/5 )+( -1 )+...= - 441/5

首項(a) 是 1/5
公差(d) 是 -2/5 - 1/5 = -3/5

用 Sn = n/2 (2a + (n-1)(d) )
-441/5 = n/2 (2(1/5) + (n-1)(-3/5) )
-441/5 = n/2 (2/5 - 3/5n + 3/5)
-441/5 = n/2 (1-3/5n)
-882/5 = n - 3/5 n^2
-3/5 n^2 +n +882/5 = 0
n = -16.3(除去) 或 18

項數是 18

b) 方法同上
a = 10x -y
d = -x-y
45x -120y = n/2 (2(10x-y) + (n-1)(-x-y) )
45x -120y = n/2 ((20x-2y)-nx-ny+x+y)
90x - 240y = n (21x -y -nx -ny)
90x - 240y = 21xn -yn- xn^2 -yn^2
0 = -xn^2 - yn^2 +21xn -yn -90x +240y
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加油!!

(a)
1/5+( -2/5 )+( -1 )+...
= 1/5 + (1/5 - 1* 3/5) + (1/5 - 2* 3/5) + ....
= n/5 - 3/5 [0+1+2+...n]
= n/5 - 3/5 [(n+1)/2 *(0+n)]
= n/5 - 3/5 [n(n+1)/2]
= n/10 [2 - 3(n+1]
= -n/10 [1+3n] = -441/5
Therefore,
n(1+3n) = 884
3n^2 +n -884 =0
(n-17)(3n-52) =0
n =17 or 52/3 (rejected)
ANS. is 17 items

(b)
(10x -y )+( 9x -2y )+( 8x -3y )+...= 45x -120y
consider -y+ -2y + -3y + ..... = -120y
-y [1+2+3 .....+n] = -120y
n/2 [1+n] = 120
n(n+1) = 240
n^2 + n - 240 = 0
(n+16)(n-15) = 0
n = -16 (rejected) or 15
ANS. is 15 items

Consider 10x + 9x +8x + ... + 0x + -1x + -2x + -kx = 45x
(k+11)/2 [10 + (-k)] =45
(k+11)(10-k)=90
-k^2 -k +110=90
k^2 +k -20=0
(k+5)(k-4) = 0
k=-5 (rejected) or 4
Therefore, total items = 11+4=15nos. (ok)