A specialized thermal probe is melting a borehole through a glacier. In the 1st hour, the probe melts a depth of 160 mm. In the 2nd hour, it melts an additional 156 mm. In the 3rd hour, it melts an additional 152 mm. The depths melted in subsequent hours form an arithmetic sequence.
Show that the probe melts an additional 92 mm in the 18th hour.
Find the total depth the probe has melted after 18 hours.
After the 18th hour, the additional depths melted each hour form a geometric sequence with common ratio rrr. In the 20th hour, the probe melts an additional 85 mm.
Find the value of rrr, giving your answer to 3 decimal places.
After a total of NNN hours, the probe will have melted a total depth of more than 4 m.
Find, showing your working, the smallest possible value of NNN.
