A carpenter makes the ladder shown. Its rungs are 20 cm apart and shrink evenly from 50 cm at the bottom to 30 cm at the top; the top and bottom rungs are 2 m apart. What total length of wood does he need for the rungs?

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 — $d=3$ ✓.