You buy a set of 9 books for $49.50. If the books are priced in increasing order with a $1 difference between the price of each book, how much did the 4th cheapest book cost?
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Thanks, this one was a nice quick arithmetic sequence problem. Took me a second to realize I could just subtract the extra dollars from the total instead of setting up x + (x+1) + ...
Same here, that shortcut saved a lot of time.
I did the long way first but still got there lol
Wait, why do we subtract from the total? I set it up with x as the cheapest and got confused with all the terms.
If x is the cheapest, the 4th cheapest is x+3. You can average it out or subtract the extras that pile up.
I got 5.50 but I want to double check. The middle book is the average, so the 5th book equals 49.50/9, then the 4th is a dollar less, right?
Yes, that's the cleanest way to see it.
This was straightforward for me once I saw the difference is constant. Good confidence booster for sequences.
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.