Should this mini-question have been clearer?
When they said "second common difference", I thought that was a little bit confusing. Should this maybe have been changed to "difference of any two consecutive terms" or something like that?
can you show a snapshot?
Hey @professionalbronco , good question! I understand where you're confused-- "common" is a bit confusing since the differences aren't the same the first time. But, there is a difference between the "difference of two consecutive terms" and the "second difference".
For example, the five few terms of sequence with formula \(2n^2+n\) are \(3,10,21,36,55\)
The difference between two consecutive terms is \(7,11,15,19\). You can think of this as the "first difference".
The differences between the terms of our new sequence \(7,11,15,19\) is \(4,4,4,4\). We just took the common difference OF the common differences, so this is the "second" difference!
Doing this process again, the third difference of the terms will be \(0,0,0\). Hope this makes sense!
@quacker88 ohh, I see. Thanks!