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 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.