Guven that a+m, a+3m and a+11m form a geometric sequence, where a and m are non-zero numbers.
a) Express m in terms of a.
b) Hence find the common ratio (R) of the geometric sequence.
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關於Geometric Sequences
2006-11-26 4:22 pm
回答 (1)
2006-11-26 4:30 pm
✔ 最佳答案
geometric sequence means their ratio are the same:(a+3m)/(a+m) = (a+11m)/(a+3m)
multiply (a+m)(a+3m) on both side:
(a+3m)(a+3m) = (a+11m)(a+m)
a^2+6ma+9m^2 = a^2+12ma+11m^2
simplify: 6ma+2m^2 = 0
so m = 0 (rejected) or m = -3a
Therefore the numbers are -2a, -8a, -32a, and the common ratio is 4.
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