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.
Practise Edexcel A Level Maths Sequences and Series with exam-style questions for A Level Maths. 156 questions covering 3.1 Arithmetic Sequences, 3.2 Arithmetic Series, 3.3 Geometric Sequences, 3.4 Geometric Series, 3.5 Sum to Infinity, 3.6 Sigma Notation, 3.7 Recurrence Relations, and 3.8 Modelling with Series, matched to the Edexcel A Level Maths (9MA0) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
