In a certain sequence, each term after the first term is one-half the previous term. If the tenth term of the sequence is between 0.0001 and 0.001, then the twelfth term of the sequence is between

Correct answer marked below

0.0025 and 0.025

0.00025 and 0.0025

0.000025 and 0.00025

Correct

0.0000025 and 0.000025

0.00000025 and 0.0000025

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Explanation

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Comments

AshitaJul 10

Wait, the sequence is halving each time, so the 12th term is 1/4 of the 10th term, right? That makes this one pretty straightforward once you see it.

NohsJul 12

Yep, just divide the interval by 4. I initially tried to set up a formula and overcomplicated it.

CiroSep 13

Got B. Just took the given range and multiplied by 0.25 since we're going two terms forward.

IshaanSep 24

Same here. Took me a second to realize we don't need the actual first term at all.

MelissaSep 16

Is it always two steps back? Like 10th to 12th is 2 terms, so factor is (1/2)^2 = 1/4. Just want to make sure I'm not off by one.

AravindSep 29

Yeah, each step multiplies by 1/2, so two steps is 1/4. You're good.

MariahJul 22

This was a nice one. The numbers look scary but the logic is simple. Good reminder to not panic at small decimals.

What this question tests

Your ability to spot and extend arithmetic and geometric sequences and work with recursive definitions.

Off-by-one errors in indexing (a₀ vs a₁) or confusing an arithmetic difference with a geometric ratio.