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 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.