# Quadratic [formula of tn, etc]

• February 12th 2009, 12:41 PM
brittt--
Hey everyone, this is my first post so I'm sorry if it's a little scattered.
We're doing quadratic sequences in class right now.
For one of my homework questions, we're asked :
Given the following information find the formula for tn.
t1=5, t3=25
So i'm a little confused on how to go about solving this.
Any help would be greatly appreciated.
• February 12th 2009, 12:53 PM
Jhevon
Quote:

Originally Posted by brittt--
Hey everyone, this is my first post so I'm sorry if it's a little scattered.
We're doing quadratic sequences in class right now.
For one of my homework questions, we're asked :
Given the following information find the formula for tn.
t1=5, t3=25
So i'm a little confused on how to go about solving this.
Any help would be greatly appreciated.

you need at least three points to make a quadratic. there are perhaps several answers that can fit this
• February 12th 2009, 12:54 PM
brittt--
So there's no way I could get a basic tn formula from just the two values?
• February 12th 2009, 01:15 PM
Jhevon
Quote:

Originally Posted by brittt--
So there's no way I could get a basic tn formula from just the two values?

of course there are ways. in fact, that's the problem, there would be too many answers. for one answer you could get $t_n = \frac 52 n^2 + \frac 52$

we get this by making the quadratic of the form $t_n = at^2 + b$ and then solving for $a$ and $b$ in two simultaneous equations using the points $(1,5)$ and $(3,25)$

we could get another answers by trying $t_n = an^2 + bn$ for instance