--DEFINITION--
"What is a quadratic sequence?"
The nth term of a quadratic sequence comes in the form of an^2 + b (e.g. 2x^2 + 3), which means that, unlike the linear sequence, the differences in the sequence are not the same (not linear), HOWEVER, the difference of the differences (second difference) are constant."
For example in the sequence 3, 6, 11, 18, 27 …
The first differences are 3, 5, 7, 9, so they are nonlinear, but...
The second differences are 2, 2, and 2 which are constant
"Now let's work out the nth term for a quadratic step-by-step!"
--WORKED EXAMPLE--
Let's use the sequence above: 3, 6, 11, 18, 27
Now let's put it in the form an^2 + b
Step 1: Identify the first difference
For 3, 6, 11, 18, 27 the first difference are
3, 5, 7, 9,
Step 2: Identify the second difference
For 3, 5, 7, 9 the 2nd difference are
2, 2, and 2
Step 3: Work out the value of 'a' using step 2
a = second difference / 2
We worked out the second difference in step 2.
So in this sequence it's a = 2/2 = 1
So if a = 1 then we have: n^2 + b
So, a = 1
Step 4: Work out the value of 'b'
Now that we know that the nth term starts with n^2, its values are 1, 4, 9, 16, 25, so the difference between the actual sequence and these values must be the value of 'b'.
Actual: 3, 6, 11, 18, 27
n^2: 1, 4, 9, 16, 25
Diff (='b'): = 2
So, b = 2
Step 5: Work out the nth term
We have:
n^2 + 2
TASK:
You will be assigned a question to work through step-by-step and post your process on the Padlet below. You may use the example given as a guide on how to structure your answer.
--WORKSHEETS--