Question

Find a polynomial function f(n) such that f(1), f(2), ... , f(8) is the following sequence.
4, 11, 18, 25, 32, 39, 46, 53

Answer 1

do you see any pattern in that sequence??

Answer 2

like if you add or subtract a particular number from the current term, you get the next term!?

Answer 3

32 and 46 are part of the sequence

Answer 4

suppose instead we have the sequece

3, 9, 15, 21, 27

Then I would use the function f(x)=3+6(x-1)

The reason I choose this is because we want to start at 3, and add on multiples of 6, but we want it so that 1->3, 2->9,3->15

To do that we need to be able to add multiples of 6 to 3, you might think well then we should use f(x) = 3+6x because that would add multiples of 6 to 3, but we want to get 3 when we put in 1, so we do the (x-1) to kill of that term (it goes to 0)

So we have f(x)=3+6(x-1) and sure enough f(1) = 3+6(1-1) = 3, f(2) = 3+6(2-1) = 9.....

Now do something similar with this :)