November 2019 1 120 Report
Two musical instruments, A and B, consist of metal bars of decreasing lengths
(1) The first bar of instrument A has length 20\;\text{cm} and the lengths of the bars form a geometric progression. The 25^{\text{th}} bar has length 5\;\text{cm}. Show that the total length of all the bars must be less than 357\;\text{cm}, no matter how many bars there are.

Instrument B consists of only 25 bars which are identical to the first 25 bars of instrument A
(2) Find the total length, L\;\text{cm}, of all the bars of instrument B and the length of the 13^{\text{th}} bar
(3) Unfortunately the manufacturer misunderstands the instructions and constructs instrument B wrongly, so that the lengths of the bars are in Arithmetic Progression with common difference d\;\text{cm}. If the total length of the 25 bars is still L\;\text{cm}, and the length of the 25^{\text{th}} bar is still 5\;\text{cm}, find the value of d and the length of the longest bar
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