In a certain quiz that consists of 10 questions, each question after the first is worth 4 points more than the preceding question. If the 10 questions on the quiz are worth a total of 360 points, how many points is the third question worth?
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Thanks, this one was a nice little arithmetic sequence warm-up. I just set the first question as x and wrote out the sum.
Same approach for me, took under a minute once I remembered the sum formula.
For some reason I kept trying to find the total of all 10 and divide, which obviously doesn't work since they aren't equal. Once I used average × number of terms it clicked.
Yeah the equal-spacing trick is the whole point of these. Average of first and last times 10 equals 360.
Is there a faster way to do this without writing out all ten terms? I got it but it felt slow.
Use the sum formula and then solve for the first term, then add the two increments. Pretty quick.
You can also think of it as the median question being the average value, then work from question 5 or 6.
Got 26 and felt good about it, then second-guessed whether they wanted the third or the first. Classic careless error trap.
I did the same thing at first, had to go back and reread the question.
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.