The sum of 49 consecutive integers is . What is their median?
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Median of an odd number of consecutive integers is just the average, so divide 7^5 by 49. 7^5/7^2 = 7^3. Not bad at all.
Yep, once you see 49 = 7^2 the rest is straightforward.
Quick q — why can we just use the mean here? For an odd count of consecutive integers the middle term equals the average, so median = mean = sum/49. That's the key idea.
Because consecutive integers are evenly spaced, so they're symmetric around the middle one.
Got it, so it works specifically because 49 is odd. Thanks!
Took me way too long because I started writing out terms like n, n+1, n+2... then realized I didn't need any of that. Just sum/count.
Same trap! I always overcomplicate sequences problems.
Careful with the answer choices — 7^5 is the sum, not the median. Easy to grab that by accident if you rush.
Yeah, E is definitely the trap answer.
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.