    This is where the difference between each number in the sequence is not the same

#### Example 1.   Find the 15th term in the sequence 2, 5, 10, 17, 26, ...

(a) Work out the first and second difference between each term

(b) Work out the formula
As the 2nd difference is the same the sequence is a quadratic, try n2

(c) Work out the 15th term:

#### Example 2.   Find the 17th term in the sequence 4, 10, 20, 34, 52, ...

(a) Work out the first and second difference between each term

(b) Work out the formula
As the 2nd difference is the same the sequence is a quadratic, try n2, then 2n2 until it is close to the values of the Nth term

(c) Work out the 17th term:

#### Example 3.   Find the 9th term in the sequence 2, 11, 26, 47, 74, ...

(a) Work out the first and second difference between each term

(b) Work out the formula
As the 2nd difference is the same the sequence is a quadratic, try n2, then 2n2 and so on... until it is close to the values of the Nth term

(c) Work out the 9th term:

Note: from the above three examples:
If the 2nd difference in (a) is equal 2, the nth term formula will include n2
If the 2nd difference in (a) is equal 4, the nth term formula will include 2n2
If the 2nd difference in (a) is equal 6, the nth term formula will include 3n2 to:  