2016台北年菜推薦 年菜食譜 , 年菜預購 , 年菜2015 , 年菜訂購 , 7 eleven年菜訂購 , 年菜宅配 , 年菜菜單 , 年菜推薦 , 年菜食譜大全 , 年菜2016 , 年菜外帶 , 外帶年菜 台中

1.
平均數 = [(a - 10) + (41a - 10)]/2 = 21a - 10
公差 = (5a - 10) - (a - 10) = 4a
項數 = {[(41a - 10) - (a - 10)]/4a} + 1 = 11
和:
11(21a - 10) = -803
21a - 10 = -73
a = -3

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2.
答案；(A) 21

首項 a₁ = a，公差 = d

a₁ + a­₂ = 23
a + a + d = 23
2a + d = 23 ... [1]

a₆ + a₇ = 5
(a + 5d) + (a + 6d) = 5
2a + 11d = 5 ... [2]

[2]-[1]:
10d = -18
d = -1.8

代入[1]中:
2a - 1.8 = 23
a = 12.4

a₃ + a₄ + a₅
= (a + 2d) + (a + 3d) + (a + 4d)
= 3a + 9d
= 3(12.4) - 9(1.8)
= 21

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3.
(1)
首項 a = a₁ = -49，公差 = d

a₁₀ = -22
a + 9d = -22
-49 + 9d = -22
d = 3

a_n > 0
a + (n - 1)d > 0
-49 + 3(n - 1) > 0
3n - 52 > 0
n > 17.33

第 18 項開始為正數。

(2)
自第 1 項加到第 17項時，其和會最小。

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4.
首項 a，公差 d = 2

a₁₀ = 20
a + 9d = 20
a + 9*2 = 20
a = 2
首項 = 2

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5.
34 - (a - 4) = (2a - 12) - 34
34 - a + 4 = 2a - 12 - 34
a = 28

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6.
12, a₂, a₃, ..., a₁₆, 36

S₁₇
= 項數 x (首項 + 末項) / 2
= 17 x (12 + 36) / 2
= 408

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7.
首項 a = 10, 公差 d = 3, 項數 n = 14

S₁₄
= n (2a + 13d) / 2
= 14 x (2 x 10 + 13 x 3) / 2
= 413

共種樹苗數目 = 413棵

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8.
項數 n = 31 + 30 + 31 + 30 = 122
首項 a = 15
公差 d = 2

S₁₂₂
= n (2a + 121d) / 2
= 122 x (2 x 15 + 121 x 2) / 2
= 16592

共存款 = 16592元

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9.
a₇₀ - a₅₇ < 0
(a + 69d) - (a + 56d) < 0
13d < 0
d < 0

(A) 正確
a₄₃ - a₆₇ = (a + 42d) - (a + 66d) = -24d > 0

(B) 錯誤
a₄₂ - a₅₁ = (a + 41d) - (a - 50d) = -9d > 0

(C) 錯誤
(a₁₈ + a₅₁) - (a₂₁ + a₄₈) = (2a +67d) - (2a + 67d) = 0
所以 a₁₈ + a₅₁= a₂₁ + a₄₈

(D) 錯誤
(a₁₂ + a₃₁) - (a₉ + a₃₄) = (2a +41d) - (2a + 41d) = 0
所以 a₁₂ + a₃₁= a₉ + a₃₄

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10.
設三角形三邊為 (a - d) 公分, a 公分和 (a + d) 公分。

(a + d)² = a² + (a - d)² ... [1]
(a + d) + a + (a - d) = 24 ... [2]

由[2]:
3a = 24
a = 8

代入[1]中:
(8 + d)² = 8² + (8 - d)²
64 + 16d + d² = 64 + 64 - 16d + d²
32d = 64
d = 2

三角形面積
= (1/2) x 8 x (8 - 2) 平方公分
= 24 平方公分

參考資料 sioieng

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