A mineral extraction team recovers a a\,a tonnes of ore in the first week. Each subsequent week, the amount extracted increases by a constant d d\,d tonnes.
The total tonnage extracted over the first 8 weeks is equal to the square of the total tonnage extracted over the first 2 weeks.
Show that 2a+7d=a2+ad+14d22a + 7d = a^2 + ad + \frac{1}{4}d^22a+7d=a2+ad+41d2
Given that the amount of ore extracted in week 5 is exactly 10 tonnes, find the smallest possible value of aaa.
308 exam-style questions on OCR A Level Maths 1.4 Sequences and Series, covering 1.4.1 Binomial expansion for positive integer n, 1.4.2 Link to binomial probabilities, 1.4.3 Binomial expansion for rational n (A-level only), 1.4.4 Validity of the expansion (A-level only), 1.4.5 Sequences (A-level only), 1.4.6 Increasing, decreasing and periodic sequences (A-level only), 1.4.7 Sigma notation (A-level only), 1.4.8 Arithmetic sequences and series (A-level only), 1.4.9 Geometric sequences and series (A-level only), 1.4.10 Sum to infinity of a geometric series (A-level only), and 1.4.11 Modelling with sequences and series (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.