At a timber depot, logs are stacked so that the bottom row has 20 logs, the row above it 19, the next 18, and so on. The stack has 165 logs in all. How many logs are in the top row?

Between two numbers a and $b$, you can insert $k$ 'arithmetic means' so that the resulting sequence is in AP.

**Setup**: a, $m$₁, $m$₂, …, $m_k,b$. Total of $k+2$ terms in AP, so:
- First term = $a$, last term = $b$.
- Common difference $d=(b-a)/(k+1)$ (because there are $k+1$ 'gaps').

**Example**: insert 3 arithmetic means between 4 and 16.
$d=(16-4)/(3+1)=3$. Means: 7, 10, 13. Check: 4, 7, 10, 13, 16 — $d=3$ ✓.