What is the fifth number in a particular sequence of numbers, if the tenth number in the sequence is 450? (1) The ninth number in the sequence is 150. (2) Each number in the sequence is three times the previous number.
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Thanks, this one was a nice quick reminder to actually check what the sequence rule is before doing any math.
Same here, I almost started calculating with just the first statement.
Yeah the trap is tempting for sure.
Wait, for statement 1, knowing the 9th term is 150 doesn't tell us anything about how the terms relate, right? We can't just assume it's arithmetic.
Exactly, that's the whole point. No fixed rule means no way to work backward to the 5th.
Right, without a pattern stated you could make the 5th term anything.
Statement 2 is enough because you can just keep dividing 450 by 3 until you reach the fifth term.
Yep, two steps back and you're there.
Got this wrong because I thought I needed both. Classic DS overthinking on an easy-ish one.
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.