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What are we doing to the first term to get the second term? if you aren't sure, solve the following for d 7 + d = 4
We are removing 3
ie subtracting 3 each time
7 - 3 = 4 4 - 3 = 1 1 - 3 = -2
then -5, then -8 right?
in general, to get the next term f(n+1) you subtract 3 from the nth term f(n+1) = f(n) - 3
yeah and it goes on forever
So it would be option C: f(1) = 7, f(n + 1) = f(n) - 4; for n ≥ 1
f(1) = 7 is given to us to find f(2) we subtract off 3 or we use the formula f(n+1) = f(n) - 3 f(n+1) = f(n) - 3 f(1+1) = f(1) - 3 ... replace each n with 1 f(2) = 7 - 3 f(2) = 4
you'll do that for n = 2, n = 3, etc
I still think it's option C
no we aren't subtracting 4 each time
I don't get this at all then
f(1) is the first term f(2) is the second term f(3) is the third term etc etc in general, the nth term is f(n). We replace n with whole numbers like n = 5 or n = 6
jumping from 7 to 4, then to 1, etc means we subtract 3 each time in general we have the nth term f(n) subtract off 3 f(n) - 3
that gives the term right after the nth term, the f(n+1) term which is why f(n+1) = f(n) - 3
look at f(n+1) = f(n) - 3 what happens when you replace every n with say n = 3
All I did was substitute 'n' with 3
saying "f(3) - 3" means "take the third term and subtract off 3" the third term is 1 so f(3) - 3 = 1 - 3 = -2 which gives us the fourth term f(4)
Ehh I give up on this. I'll just guess the answer because I'm still as confused as I was in the beginning. I'm sorry for completely wasting your time :/ Thank you very much though.
do you see how f(n) is the nth term?