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Nth Term of a Quadratic Sequence

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

Example 2