Homework Help: Find the equation of the curve

1. Nov 7, 2011

aerin8

1. The problem statement, all variables and given/known data
From the given sequence of numbers (11.25, 10, 9.25, 9, 9.25, 10, 11.25, 13, 15.25, 18 ...)
A) Graph the sequence
B) Find the equation of the curve
C) Determine the 100th term of the sequence

2. Relevant equations

3. The attempt at a solution
I know how to graph the sequence by setting the given numbers as y coordinates and their order as x coordinate but beyond there I'm stuck. Help please!

2. Nov 7, 2011

Staff: Mentor

There is a certain pattern that jumps out here. Look at the difference of successive terms in this sequence.

Also, the second differences are constant.

3. Nov 7, 2011

aerin8

I can see the pattern but I don't know how to apply it in the equation of the curve. Is there a formula I can plug the data into to find the equation?

4. Nov 7, 2011

aerin8

is the curve the same thing as a parabola?

5. Nov 7, 2011

Staff: Mentor

The curve might be a parabola. If so, you know where the vertex is.

In case it's not a parabola, there's an area of mathematics called Difference Equations (see http://en.wikipedia.org/wiki/Recurrence_relation) that might be helpful. See especially the section titled "Relationship to difference equations narrowly defined."