Maria is crafting a bracelet using beads in a sequence of yellow, pink, teal, brown, and gray. If the 1st bead is yellow, what color will the 187th bead be?
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good question
Thanks
Wait, is it really this easy? Just divide 187 by 5 and use the remainder? Got pink, moving on lol
yep exactly, 5-color cycle so just the remainder matters
thanks! the pattern of 5 colors threw me for a sec but n = 187 with a remainder makes it click
Quick trick: since it cycles every 5, just think about where 187 lands near the end. 185 would finish a full cycle, so the 187th is the 2nd in the pattern.
oh that's a nicer way than doing long division, thanks
hmm does that always work or just when the remainder is small?
Is it 187 mod 5? I keep getting confused on whether the first bead counts as position 1 or 0.
it's position 1, so remainder 1 = yellow, remainder 2 = pink, etc
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.