A specialized geothermal drill is used to penetrate a layer of hard rock. During the 1st minute of drilling, the drill penetrates 160 cm. During the 2nd minute, it penetrates an additional 157 cm. During the 3rd minute, it penetrates an additional 154 cm. The additional depths penetrated in subsequent minutes form an arithmetic sequence.
Show that the drill penetrates an additional 100 cm during the 21st minute.
Find the total depth the drill has penetrated after the 21st minute.
After the 21st minute, the additional depths penetrated in each minute form a geometric sequence with common ratio rrr. On the 23rd minute, the drill penetrates an additional 94 cm.
Find the value of rrr, giving your answer to 3 decimal places.
After a total of N N\,N minutes, the drill will have penetrated a total depth of more than 50 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.