標題:
HKDSE Maths
發問:
The sume of the 4th term and the 5th term of a geometric sequence is -4. If the sum of the first two terms is 32, find the first term of the sequence.
最佳解答:
4th + 5th = ar3 + ar ?= - 4 ...... (1)1st + 2nd = a + ar = 32 ...... (2) (1) / (2) :( ar3 + ar ?) / (a + ar) = - 4 / 32 ar3 (1 + r) / ( a (1 + r) ) = - 1/8 r3 = - 1/8 r = - 1/2 Sub. into (2) :a + a(- 1/2) = 32 a/2 = 32 a = 64 The first term of the sequence is 64.
其他解答:
如果是應付選擇題（multiple choice），以下是最快的方法： 公式： y / ( 1 + ( x/y ) ^ ( 1/d ) ) ＝ 32 / ( 1 + (-4/32) ^ (1/3) ） ＝ 64 熟練的同學應該可以十秒內準確地完成題目。 詳情： 先將題目變為： The sum of the (d + 1) th term and the (d + 2) th term of a geometric sequence is x. If the sum of the first two terms is y. 在此題目， (d＋1)＝4 (d+2) = 5 d＝3 x = -4 y = 32 The first term of the sequence = y / ( 1 + ( x/y ) ^ ( 1/d ) ) ＝ 32 / ( 1 + (-4/32) ^ (1/3) ） ＝ 32 / ( 1 + (-1/8) ^ (1/3) ） ＝ 32 / ( 1 + (-1/2) ） ＝ 32 / ( 1 - 1/2) ＝ 32 / ( 1/2 ) ＝ 32 / ( 0.5 ) ＝ 64 註： (-1/8) ^ (1/3) 的意思是 負八份之一的開方三次 即係負二份之一（i.e. -1/2) 同學可以到以下網址練習此類題目： http://www.ktlam.hk/hkmath/index/d3dc2f17
HKDSE Maths
發問:
The sume of the 4th term and the 5th term of a geometric sequence is -4. If the sum of the first two terms is 32, find the first term of the sequence.
最佳解答:
4th + 5th = ar3 + ar ?= - 4 ...... (1)1st + 2nd = a + ar = 32 ...... (2) (1) / (2) :( ar3 + ar ?) / (a + ar) = - 4 / 32 ar3 (1 + r) / ( a (1 + r) ) = - 1/8 r3 = - 1/8 r = - 1/2 Sub. into (2) :a + a(- 1/2) = 32 a/2 = 32 a = 64 The first term of the sequence is 64.
其他解答:
如果是應付選擇題（multiple choice），以下是最快的方法： 公式： y / ( 1 + ( x/y ) ^ ( 1/d ) ) ＝ 32 / ( 1 + (-4/32) ^ (1/3) ） ＝ 64 熟練的同學應該可以十秒內準確地完成題目。 詳情： 先將題目變為： The sum of the (d + 1) th term and the (d + 2) th term of a geometric sequence is x. If the sum of the first two terms is y. 在此題目， (d＋1)＝4 (d+2) = 5 d＝3 x = -4 y = 32 The first term of the sequence = y / ( 1 + ( x/y ) ^ ( 1/d ) ) ＝ 32 / ( 1 + (-4/32) ^ (1/3) ） ＝ 32 / ( 1 + (-1/8) ^ (1/3) ） ＝ 32 / ( 1 + (-1/2) ） ＝ 32 / ( 1 - 1/2) ＝ 32 / ( 1/2 ) ＝ 32 / ( 0.5 ) ＝ 64 註： (-1/8) ^ (1/3) 的意思是 負八份之一的開方三次 即係負二份之一（i.e. -1/2) 同學可以到以下網址練習此類題目： http://www.ktlam.hk/hkmath/index/d3dc2f17
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