Using the full second difference instead of half H
"The Half Slip"
The Mistake in Action
Find the nth term of 1, 4, 9, 16, 25, ...
Second differences = 2
Wrong: nth term = $2n^2 + ...$
Why It Happens
Students correctly find the second difference is 2, but forget to halve it to get the coefficient of $n^2$.
The Fix
For a quadratic sequence $an^2 + bn + c$:
$$a = \frac{\text{second difference}}{2}$$
If second difference = 2, then $a = \frac{2}{2} = 1$
For 1, 4, 9, 16, 25, ...: This is actually $n^2$ (the square numbers)!
nth term = $n^2$ (or $1n^2 + 0n + 0$)
Spot the Mistake
Can you identify where this student went wrong?
Second differences = 2
nth term = $2n^2 + ...$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: