Quadratic sequences

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

Golden rule

• 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

Working it out

• 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