### Quadratic Sequences

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

- Example 1. Find the 15
^{th}term in the sequence 2, 5, 10, 17, 26, ... - Example 2. Find the 17
^{th}term in the sequence 4, 10, 20, 34, 52, ... - Example 3. Find the 9
^{th}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 2^{nd} difference is the same the sequence is a quadratic, try n^{2}

**(c)** Work out the 15^{th} term:

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

**(b)** Work out the formula

As the 2^{nd} difference is the same the sequence is a quadratic, try n^{2}, then 2n^{2} until it is close to the values of the Nth term

**(c)** Work out the 17^{th} term:

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

**(b)** Work out the formula

As the 2^{nd} difference is the same the sequence is a quadratic, try n^{2}, then 2n^{2} and so on... until it is close to the values of the Nth term

**(c)** Work out the 9^{th} term:

Note: from the above three examples:

If the 2^{nd} difference in (a) is equal 2, the n^{th} term formula will include n^{2}

If the 2^{nd} difference in (a) is equal 4, the n^{th} term formula will include 2n^{2}

If the 2^{nd} difference in (a) is equal 6, the n^{th} term formula will include 3n^{2}

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