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 (MEI) A Level Maths 1.6 Sequences and Series, covering 1.6.1 Binomial expansion for positive integer n, 1.6.2 Factorial and combinations notation, 1.6.3 Binomial expansion for rational n (A-level only), 1.6.4 Binomial expansion of (a + bx)^n via factoring (A-level only), 1.6.5 Binomial approximating polynomials (A-level only), 1.6.6 What a sequence is; finite and infinite (A-level only), 1.6.7 Generate a sequence by formula or recurrence (A-level only), 1.6.8 A series as a sum of terms (A-level only), 1.6.9 Sigma notation (A-level only), 1.6.10 Increasing, decreasing and periodic sequences (A-level only), 1.6.11 Convergent and divergent sequences (A-level only), 1.6.12 Arithmetic sequences and series (A-level only), 1.6.13 Standard formulae for arithmetic series (A-level only), 1.6.14 Geometric sequences and series (A-level only), 1.6.15 Standard formulae for geometric series (A-level only), 1.6.16 Sum to infinity of a geometric series (A-level only), and 1.6.17 Sequences and series in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.