Set A consists of the first 10 terms of a sequence. For which sequence, in which defines how the nth term is calculated, will set A have the greatest standard deviation?
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Is it just me or does this question look way harder than 555-605? I spent 3 minutes trying to compute SD for each one before realizing I could just compare the spread.
Same! The key is that SD only depends on the spread, not the actual values, so constants like +50 or -60 don't matter at all.
Quick tip: SD measures spread, so adding or subtracting a constant shifts all terms but doesn't change the SD. That instantly kills choices B and E (same spread as each other) and makes D equivalent to C.
Exactly, and between n^2 and n^3, n^3 grows much faster, so the values are more spread out.
For the first 10 terms, n^3 goes from 1 to 1000. That's a huge range compared to n^2 which only goes to 100. So C should have the largest SD.
Wait, but what about the constant -60 in option D? Does that affect anything? I keep second-guessing myself.
Nope, subtracting a constant from every term just shifts the whole set. The distances between terms stay the same, so SD is unchanged.
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.