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**

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 formSo our aim is to find values for

a,bandc. For this we will use the facts below about quadratic sequences.Suppose you have the following quadratic sequence:

STEP 1: Find the 1st difference & the 2nd differenceSTEP 2: Calculate a, b and cUsing algebra, calculate constants a, b and c of the nth term formula

Example 2## Nouri Dib