Question
If a1 = 1 and an+1 – 3an + 2 = 4n for every positive integer n, then a100 equals (CAT 2005)
Answer: Option C
:
C
Option (c)Shortcut: Double SubstitutionWrite each answer option in terms of n (where n=100)3n-1 – 2n3n-1 + 2n3n - 2n3n + 2nNow at n=1, we should get 1. Put n=1 in the answer options and eliminate those options where you do not get 1-1 ≠12 ≠115≠1 thus, the answer is option (c)
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:
C
Option (c)Shortcut: Double SubstitutionWrite each answer option in terms of n (where n=100)3n-1 – 2n3n-1 + 2n3n - 2n3n + 2nNow at n=1, we should get 1. Put n=1 in the answer options and eliminate those options where you do not get 1-1 ≠12 ≠115≠1 thus, the answer is option (c)
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