Find the equation of the curve

[aerin8]

Homework Statement

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

Homework Equations

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!

 

[Mark44]

Homework Statement

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

Homework Equations

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!

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.

 

[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?

 

[aerin8]

is the curve the same thing as a parabola?

 

[Mark44]

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."