How do you find out the nth term in quadratic sequences?

Answer 1

It's simpler than you might think..

The general equation you need is this:

a+b+c 4a+2b+c 9a+3b+c 16a+4b+c

3a+b 5a+b 7a+b

2a 2a

Basically, the second row down is the difference between the terms of the sequence itself (top row). And the 3rd row down is the differences of the differences (:P).

I'm not good enough with words to explain how to find the nth term so I'll give you an example:

3 7 15 27 43

4 8 12 16

4 4 4

First, you need to know this formula:

2a=diff. of diff. (4 in this example)

3a+b= 1st of the differences (4 in this example)

A+B+C= 1st term (3 in this example)

So let's work it out:

2a=4

(so) a=2

3a+b= 4

(3a would be 3 times 2 so) 6+b=4

(To get from 6 to 4 you need to minus two so) b= -2

(To get to c you need a+b and then work out the difference of that and the 1st term.)

a+b= 0

(2-2= 0)

(The difference of the first term and a+b gives you c)

3-0= 3

c=3

Hope this has helped :S