標題:
F5_maths(a.s.同g.s.)兩條廿分
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發問:
Q1:the infinite sum of a g.s. is 4 and the infinite sum of the cubes of its termsis equal to 192.find the first term and the common ratio.Q2:the sum to infinite geometric sequence is 16 and the sum to infinity of the squares of its term is 768/5. find the common ratio and the fourth termof the... 顯示更多 Q1:the infinite sum of a g.s. is 4 and the infinite sum of the cubes of its terms is equal to 192. find the first term and the common ratio. Q2:the sum to infinite geometric sequence is 16 and the sum to infinity of the squares of its term is 768/5. find the common ratio and the fourth term of the sequence. 我諗兩條問既野十分類似..但係我諗唔到點計,書又冇example
最佳解答:
(1) Let a and R be the first term and common ratio of the original G.S. respectively, then we have: a/(1 - R) = 4 ... (1) Now, for the new G.S., a3 and R3 are the first term and common ratio respectively, so a3/(1 - R3) = 192 ... (2) From (1): a/(1 - R) = 4 a3/(1 - R)3 = 64 ... (3) (2)/(3): (1 - R)3/(1 - R3) = 3 1 - 3R + 3R2 - R3 = 3 - 3R3 2R3 + 3R2 - 3R - 2 = 0 R = 1 or -1/2 or -2 Since -1
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