1. Patterning formula help!

Hello if anyone can help me with this I will be so glad. I've spent two hours straight working on it and I can't figure it out. It's due tomorrow and I am stressing!

Okay so I need an algebraic equation for this chart.

Term Number Term Value
1 ---------------- 6
2 --------------- 12
3 --------------- 20
4 --------------- 30
5--------------- 42
6 ---------------56
7----------------72

Thanks so much

2. Originally Posted by nattie
Hello if anyone can help me with this I will be so glad. I've spent two hours straight working on it and I can't figure it out. It's due tomorrow and I am stressing!

Okay so I need an algebraic equation for this chart.

Term Number Term Value
1 ---------------- 6
2 --------------- 12
3 --------------- 20
4 --------------- 30
5--------------- 42
6 ---------------56
7----------------72

Thanks so much
using the "algebraic method" or maybe A algebraic method, i found out about here, we realize that a quadratic will hit all the points.

so we will assume that $\displaystyle y = ax^2 + bx + c$

where $\displaystyle x$ is the term number, and $\displaystyle y$ is the term value.

we can set up 3 simultaneous equations to solve for $\displaystyle a,b, \mbox{ and }c$ using the first three points: $\displaystyle (1,6), (2,12), \mbox{ and }(3,20)$

now continue