Quadratic sequences

If the nth term of a sequence contains an n^2 term and no high er power of n, it is called a quadratic sequence
You can write the nth term of a quadratic sequence as:
- Un = an^2 + bn + c
Where a, b, c are numbers and a is not 0
You need to be able to find the nth term of a quadratic sequence
You can use the golden rule on the right to help

The second difference of a quadratic sequence are constant
The quadratic sequence with nth term Un =n an^2 + bn+ c has second difference equal to 2a

Start by writing out the number of coins in each pattern as a number sequence.
You are told the sequence is quadratic so you know the second difference will be constant
The coefficient of n^2 in the nth term is half of the second difference
The second difference are a, so the value of ab is 0.5
Once you have worked out the value of a, draw a table
- You need to compare the values of the terms Un with the quadratic you have
- This will help you find the rest of the nth term
- Add a row for Un - an^2
- This row will form an arithmetic sequence with nth term bn + c
- The arithmetic sequence has an nth term
- This is the last past of the nth term of the quadratic sequence
- Then check you have the write answer