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, up to and including the 18th hour, 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.
From the 18th hour onwards, 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.
305 exam-style questions on AQA A Level Maths 1.7 D: Sequences and series, covering 1.7.1 Binomial expansion, 1.7.2 Types of sequence (A-level only), 1.7.3 Sigma notation (A-level only), 1.7.4 Arithmetic sequences and series (A-level only), 1.7.5 Geometric sequences and series (A-level only), and 1.7.6 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.