F5 math problems (Geometric sequence)
2017/06/13 03:41
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F5 math problems (Geometric sequence)
發問:
Find two geometric sequences up to the fifth terms for which the fourth term is 27 and the sum of the third and the fifth terms is 117/2.
the fourth term is 27 let r be the common ratio, the third term is 27/r the fifth term is 27r 27/r + 27r = 117/2 6+6r^2 = 13r 6r^2 - 13r + 6 = 0 (2r - 3) (3r - 2) = 0 r = 3/2 or 2/3 when r = 3/2 the geometric sequence is 8, 12, 18, 27, 81/2, ... when r = 2/3 the geometric sequence is 729/8, 243/4, 81/2, 27, 18, ...
其他解答:
F5 math problems (Geometric sequence)
發問:
Find two geometric sequences up to the fifth terms for which the fourth term is 27 and the sum of the third and the fifth terms is 117/2.
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最佳解答:the fourth term is 27 let r be the common ratio, the third term is 27/r the fifth term is 27r 27/r + 27r = 117/2 6+6r^2 = 13r 6r^2 - 13r + 6 = 0 (2r - 3) (3r - 2) = 0 r = 3/2 or 2/3 when r = 3/2 the geometric sequence is 8, 12, 18, 27, 81/2, ... when r = 2/3 the geometric sequence is 729/8, 243/4, 81/2, 27, 18, ...
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