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, 94
Look at the difference between two consecutive numbers. Subtract the lowest from the highest.
If the difference is changing then this is a quadratic sequence.
Look at the difference between the differences (known as the second difference).
There is a pattern between the first differences.
The second difference is +6. This means that the sequence is quadratic.

The coefficient of n squared is always half of the second difference, which is 3n squared.
The next step is for us to subtract the n squared term from the original sequence to find the difference.
Write out the original sequence again and below it write down the values of 3n squared.
Subtract these two values to calculate the difference.

This difference creates a new sequence (3, 7, 11, 15, 19). This is an arithmetic sequence and is linear.
The difference is plus 4, so the nth term is related to the 4 times table.
Compare the sequence with the numbers in the 4 times table.
What is the difference between the 4 times table number and the sequence number.

This gives a constant difference of -1.
The nth term expression is 3n squared + 4n -1

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

3) Write down an expression for the nth term of this quadratic sequence ?
1, 3, 7, 13, 21

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

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

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