標題:
Maths_等差級數
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發問:
In a pile(堆) of sticks(棒), there are 32 sticks in the bottom layer(底層), 29 sticks in the second bottom layer, 26 sticks in the thind bottom layer, and so on. There are ten layer in the pile. The uppermost(最上) 6 layers are used to make a fence(籬笆). Finda) the number of sticks in the pile.b) the number of... 顯示更多 In a pile(堆) of sticks(棒), there are 32 sticks in the bottom layer(底層), 29 sticks in the second bottom layer, 26 sticks in the thind bottom layer, and so on. There are ten layer in the pile. The uppermost(最上) 6 layers are used to make a fence(籬笆). Find a) the number of sticks in the pile. b) the number of sticks used to make the fence
最佳解答:
T(1) = 32 T(2) = 29 T(3) = 26. Since this is an A.S., first term = a = 32 2nd term = a + d = 29, so d = -3. Now n = 10, so Sum of all sticks = (10)/2[2 x 32 + (10-1) x (-3)] = 5[64 - 27] = 5 x 37 = 185. Sum of T(1) to T(4) = (4/2)[2 x 32 + (4 -1) x (-3)] = (4/2)[64 - 9] = 110. So sticks used for the fence = total sticks - 110 = 185 - 110 = 75.
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