Arithmetic Slices - Counting Insight

If you have an arithmetic sequence of length $k$ (where $k \geq 3$), how many arithmetic subarrays does it contain?

For $k = 3$: just $1$ (the whole sequence). For $k = 4$: $3$ subarrays (length 3 at positions 0-2 and 1-3, plus length 4). For $k = 5$: $6$ subarrays.

The pattern: $1, 3, 6, 10, ...$, which is $1 + 2 + 3 + ... + (k-2) = \frac{(k-2)(k-1)}{2}$. This is a summation formula in disguise.