7 A tool for putting fence posts into the ground is called a 'post-rammer'. The distances in millimetres that the post sinks into the ground on each impact of the post-rammer follow a geometric progression. The first three impacts cause the post to sink into the ground by \(50 \mathrm {~mm} , 40 \mathrm {~mm}\) and 32 mm respectively.

1. Verify that the 9th impact is the first in which the post sinks less than 10 mm into the ground.
2. Find, to the nearest millimetre, the total depth of the post in the ground after 20 impacts.
3. Find the greatest total depth in the ground which could theoretically be achieved.