An experimental bioreactor produces biomass at a rate that varies each week. The mass of biomass produced during the nnn-th week follows an arithmetic sequence with first term a a\,a kg and common difference d d\,d kg. The total mass of biomass produced during the first 15 weeks of the operation is 1035 kg.
Show that 4a+28d=2764a + 28d = 2764a+28d=276
Given that the total mass of biomass produced during the first 45 weeks is 405 kg, calculate the total mass produced during the first 25 weeks.
Mn M_n\,Mn is the total mass of biomass produced during the first n n\,n weeks. Explain why the value you found in part (b) is the maximum value of MnM_nMn.
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.