Quadratic Sequence

A sequence of numbers when the rule is based on the second difference and is adding or subtracting the same number every time.

1) Write down an expression for the nth term of this quadratic sequence ?
6, 19, 38, 63

Look at the difference between the consecutive numbers.
If the difference is changing then this is not an arithmetic sequence.
Look at the difference between the differences (known as the second difference).
The 2nd difference is +6. This means that the sequence is quadratic.
The coefficient of n² is always half of the second difference.
In this example (6/2 = 3) so we have 3n².
The next step is for us to subtract the 3n² term from the original sequence to find the difference.
Subtract these two values to create a new sequence.

This difference creates a new sequence (3, 7, 11, 15, 19). This is an arithmetic sequence and is linear.
The difference between the consecutive numbers is 4, so the nth term is related to the 4 times table.
Compare the sequence with the numbers in the 4 times table.
How do we get from the value in the 4 times table to the number in the sequence.
This gives a constant difference of -1.
The nth term expression is 3n² + 4n -1

2) Write down an expression for the nth term of this quadratic sequence ?
2, 5, 10, 17, 26

The nth term expression is n² + 1

3) Write down an expression for the nth term of this quadratic sequence ?
-3, 0, 5, 12

4) Write down an expression for the nth term of this quadratic sequence ?
1, 3, 7, 13,

5) Write down an expression for the nth term of this quadratic sequence ?
1, 4, 9, 16

6) Write down an expression for the nth term of this quadratic sequence ?
3, 12, 27, 48

7) Write down an expression for the nth term of this quadratic sequence ?
2, 5, 10, 17

8) Write down an expression for the nth term of this quadratic sequence ?
8, 11, 16, 23

9) Write down an expression for the nth term of this quadratic sequence ?
3, 7, 13, 21

10) Write down an expression for the nth term of this quadratic sequence ?
5, 13, 25, 41

11) Write down an expression for the nth term of this quadratic sequence ?
7, 16, 27, 40

12) Write down an expression for the nth term of this quadratic sequence ?
0, 1, 4, 9

13) Write down an expression for the nth term of this quadratic sequence ?
-5, 8, 27, 52