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 = 2a FACT #2: 2nd TERM - 1st TERM = 3a + b FACT #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