A vertical farm designs its irrigation system based on the number of seedling trays in each tier. The number of trays in the first three tiers is given by the expressions:
2k+5,4k−2,8k−23 2k + 5, \quad 4k - 2, \quad 8k - 23 2k+5,4k−2,8k−23Show that k=7k = 7k=7 is the only value for which these expressions form an arithmetic sequence.
Write down the number of trays in the first tier.
Determine the common difference of the sequence representing the number of trays per tier.
The total number of trays in the first NNN tiers is denoted by SNS_NSN. Given that
SN<80 000 S_N < 80\,000 SN<80000 SN+1>80 000 S_{N+1} > 80\,000 SN+1>80000find the value of NNN.
Practise AQA A Level Maths 1.7 D: Sequences and series with exam-style questions for A Level Maths. 267 questions 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), matched to the AQA A Level Maths (7357) 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.
