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he sequence An satisfies An = An-1An-2, where n is a positiv

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he sequence An satisfies An = An-1An-2, where n is a positiv

by Max@Math Revolution » Thu Jun 06, 2019 4:50 pm

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[GMAT math practice question]

The sequence An satisfies An = An-1/An-2, where n is a positive integer greater than 2. If A1=1 and A2=2, then A123=?

A. 1/2
B. 1/4
C. 1
D. 2
E. 4
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by Max@Math Revolution » Sun Jun 09, 2019 5:10 pm
=>

A1 = 1
A2 = 2
A3 = A2/A1 = 2/1 =2
A4 = A3/A2 = 2/2 =1
A5 = A4/A3 = 1/2
A6 = A5/A4 = (1/2)/1 = 1/2
A7 = A6/A5 = (1/2)/(1/2) =1
A8 = A7/A8 = 1/(1/2) = 2
Since A7 = 1 and A8 = 2, the sequence is periodic with period 6.
Thus, A123 = A3 = 2 since 123=6·20+3

Therefore, the answer is D.
Answer: D
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