Essentially, we want to look at how the sequence is changing from term to term, and then we want to see how the changes are changing.
The sequence we've been given is
-12, -5, 12, 39, 76
First, we can find the "raw" increases - how much do we increase by as we go forward? Here's what we find:
- From -12 to -5: +7
- From -5 to 12: +17
- From 12 to 39: + 27
- From 39 to 76: +37
This gives us a new sequence to look at: 7, 17, 27, 37. If we try the same thing on this one:
- 7 to 17: +10
- 17 to 27: +10
- 27 to 37: +10
We always add 10 from one term to the next. What this means is that, as far as the original sequence goes, we start by adding 7 and then add 10 extra every time we move forward.
This means that yes, the sequence is equal to the previous term plus a regularly increasing amount.
