Question 217540: Hi! Given a sequence like this:
when n=1, x=1
when n=2, x=5
when n=3, x=9
when n=4, x=13
... and so on, how do you come up with an equation to represent that relationship? I know the answer is 4n-3=x because I looked it up in the back of the book. But how do you figure that out on your own?
Please help! thank you!
cherilyn
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! the difference between two consecutive values of x is always 4 ___ 1 & 5, 5 & 9, 9 & 13
this makes the series arithmetic (as opposed to geometric) and 4 is the "constant difference"
so, 4n + ? = x ___ the ? is what I call the "fudge factor" ___ you can find it by just taking a pair of n and x values
4(2) + ? = 5 ___ 8 + ? = 5 ___ ? = -3
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