What is the sum of the first 100 positive odd numbers?
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Wait—is there a formula we should memorize for this? I just added 1+3+5 and saw the pattern of perfect squares, but I'm not sure that's the 'right' way to do it on the actual test.
Yeah the pattern is n^2 for the first n odd numbers, so just square the count. No need to actually add them.
Got it, that saves so much time. I was about to list them all out like an idiot lol.
I got D but honestly I almost picked A because I squared 50 instead of 100. Classic careless mistake.
Same trap! 100 odd numbers means the last one is 199, not 99. Easy to mix up.
This one is pretty straightforward if you know the sum of first n odds = n^2. Good confidence booster for sequences.
Can someone explain why the sum of consecutive odds gives a perfect square? I know the trick but I never understood the intuition behind it.
Think of it as adding an L-shaped layer each time: 1, then 3 more dots to make a 2x2, then 5 more for 3x3, etc.
That visual actually helps a lot, thanks.
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.