Compare geometric and arithmetic instrument bars

Instruments A and B have bars of decreasing lengths.

(i) A has first bar $20$ cm and a GP of lengths; its 25th bar is $5$ cm. Show the total length is less than $357$ cm, however many bars there are.

B has the first 25 identical bars from A. (ii) Find its total $L$ and its 13th bar length.

(iii) A mistaken B has 25 AP lengths, the same total $L$, and last bar still $5$ cm. Find its common difference $d$ and longest bar.