If the 1st term of a sequence is 0 and the 2nd term is 1, is the 5th term 2? (1) Each odd-numbered term is either 0 or 2. (2) The 3rd term is 2. DS11602.01
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Got this one wrong at first because I assumed the sequence had to follow some pattern. Took me a second to realize the statements don't actually lock down the 5th term.
Same! I kept trying to force a formula onto it. Once I just listed out what each statement allows, it got clearer.
Can someone explain why statement 2 alone isn't enough? I feel like if the 3rd term is 2 that tells us something about the rest.
Because nothing connects term 3 to term 5 unless you assume a pattern the question never gives you. The problem only restricts odd terms in statement 1, not statement 2.
Medium difficulty for me. Statement 1 is the tricky one — "either 0 or 2" means the 5th term could be 0 or 2, so it's not pinned down.
Right, and that's exactly the trap. It sounds restrictive until you notice both values are still allowed.
Thanks for posting this. The odd/even term language tripped me up, but breaking it into what each statement actually allows made it manageable.
What it tests
Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.
Common trap
Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.