解答

S100 = 50, S200 = 50 + 60 = 110
a100 = a1 + 99d, a200 = a1 + 199d

S100 = [a1 + (a1 + 99d)] * 100 / 2 = 50
2*a1 + 99d = 1 ...(1)

S200 = [a1 + (a1 + 199d)] * 200 / 2 = 110
10*(2*a1 + 199d) = 11
20*a1 + 1990d = 11 ...(2)

(1)*10可得:
20*a1 + 990d = 10 ...(3)
(2) - (3)可得:
1000d = 1, d = 1/1000 代入(1)可得:
2*a1 = 1 - 99d = 1 - 99/1000 = 901/1000
a1 = 901/2000

a400 = a1 + 399d = 901/2000 + 399* 1/1000 = (901+798)/2000
= 1699/2000

S400 = (901/2000 + 1699/2000) * 400 / 2
= 2600/2000 * 200 = 260

所求 = 260 - 60 - 50 = 150

Ans: 150 #

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