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Current time:0:00Total duration:2:21

Jill looked at the following sequence 0 3 8 15 24 35 and it just keeps going I guess with the dot dot dot she saw that the numbers were each one less than a square number 0 is 1 less than 1 which is a square number 3 is 1 less than 4 8 is 1 less than 9 15 is 1 less than 16 yeah they're all 1 less than a square number and conjectured that the nth number would be N squared minus 1 now conjecture that sounds like a very fancy word when someone makes a conjecture they conjectured that just means that they're making a statement that seems or they're making a proposition that seems likely to be true seems like a very reasonable thing to say but it's not definitely true so she conjectured that the nth number would be N squared minus 1 the reason why this isn't a conjecture well the reason why this is a conjecture as opposed to a a 100% definitely true statement is we don't know whether this pattern continues she's just going off of the pattern that she saw so far and she just generalized it she just assumes that it keeps on going but we don't know whether it necessarily keeps going maybe the next number it's not you would expect it to be 48 but maybe it's not 48 maybe it's something weird maybe it's 2 maybe it's 500 and so the conjecture wouldn't hold up if you were to see that but based on the evidence you see so far it seems completely reasonable that this pattern would continue and so she conjectured that the nth number would be N squared minus 1 completely reasonable now did you'll use inductive reasoning did you'll use inductive reasoning yes she used inductive reasoning that's what inductive reasoning is you see a pattern in this case every every pet every term in this sequence so far was if it's the end of the third term it was 3 squared minus 1 the fourth term is 4 squared minus 1 v squared is the fifth term is 5 squared minus 1 so she saw the pattern and she just generalized it to say well I think I've conjectured that the nth number will be N squared minus 1 that's what inductive reasoning is all about you're not always going to be a hundred percent you're you definitely won't be a hundred percent sure that you're right that the nth number will be N squared minus one but based on the pattern you so far it's a completely reasonable thing to I guess you could say to induce