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.
