Choosen As Best Answer

a + (a+2d) + (a+4d) + (a+6d) + (a+8d) = 240 ...(1)
(a+d) + (a+3d) + (a+5d) + (a+7d) + (a+9d) = 280 ...(2)
(2)-(1)可得
5d = 40, d = 8
而(1)又可整理成 5a + 20d = 240
=> 5a = 240 - 160 = 80
=> a = 16 #

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從最大邊往最小邊遞減 d = -3、首項 = a = 22
an = 22 + (n-1)×(-3) = 25 - 3n
(22 + 25 -3n) × n ÷ 2 = 70
n(47 -3n) = 140
3n^2 - 47n + 140 = 0 ※ n^2 = 平方
(n-4)(3n-35) = 0
n = 4 or 35/3(不合,第幾項不會是分數)
=> 共有 4 個邊 #

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Sn = 2n^2 + 3n
(1)
S1 = a1 = 5 #

(2)
a18 = S18 - S17
= (2 × 18^2 + 3 × 18) - (2 × 17^2 + 3 × 17)
= 702 - 629 = 73 #

(3)
a18 = a1 + 17d
5 + 17d = 73
=> d = 4 #

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把頭尾也順便算進去,總共有 12 + 2 = 14 項
(15 + m) × 14 ÷ 2 = 450 + 15 + m
7m + 105 = m + 465
6m = 360
=> m = 60 #

謝謝

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