This is one method of working out the nth term of a quadratic sequence. Other methods are also possible.

Now, just as linear sequence has an nth term of the form **an + b** ; a quadratic sequence will have an nth term of the form

So our aim is to find values for **a**, **b** and **c**. For this we will use the facts below about quadratic sequences.

With a quadratic sequence, the following is always true:FACT #1: 2nd difference = 2aFACT #2: 2nd TERM - 1st TERM = 3a + bFACT #3: 1st TERM = a + b + c

Suppose you have the following quadratic sequence:

**STEP 1**: Find the 1st difference & the 2nd difference

**STEP 2**: Calculate a, b and c

Using algebra, calculate constants a, b and c of the nth term formula

**Example 2**