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.
308 exam-style questions on OCR (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.