Max@Math Revolution wrote:[GMAT math practice question]
If An=An-1/An-2 (n3), A1=1, and A2=-2, then A100=?
A. 1
B. -1
C. 2
D. -2
E. -1/2
A� = 1
Aâ‚‚ = -2
A₃ = -2/1 = -2
Aâ‚„ = -2/-2 = 1
Aâ‚… = 1/-2 = -0.5
A₆ = -0.5/1 = -0.5
A₇ = -0.5/-0.5 = 1
A₈ = 1/-0.5 = -2
As illustrated by the results in blue, A� through A₆ represent one complete 6-term CYCLE:
1, -2, -2, 1, -0.5, -0.5
Starting with A₇ and A₈, the 6-term cycle begins again:
1, -2...
Since 6*16 = 96, the 96th term is the end of the 16th 6-term cycle.
Starting with A₉₇, the 6-term cycle begins again:
A₉₇ = 1
A₉₈ = -2
A₉₉ = -2
A�₀₀ = 1
The correct answer is
A.
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