In a sustainable construction project, the number of solar panels installed during each of the first three months is represented by the following expressions:
4k−1,7k−5,12k−19 4k - 1, \quad 7k - 5, \quad 12k - 19 4k−1,7k−5,12k−19Show that k=5k = 5k=5 is the unique value for which these monthly installation figures form an arithmetic sequence.
State the number of panels installed in the first month.
Determine the common difference for this sequence.
The total number of solar panels installed after NNN months is given by SNS_NSN.
Given that
SN<25 000 S_N < 25\,000 SN<25000 SN+1>25 000 S_{N+1} > 25\,000 SN+1>25000Find the value of NNN.
