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3 Unit A2 1: Pure Mathematics (A-level only)

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Question 139

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−19
a.

Show that k=5k = 5k=5 is the unique value for which these monthly installation figures form an arithmetic sequence.

[3]
bi.

State the number of panels installed in the first month.

[1]
bii.

Determine the common difference for this sequence.

[1]
c.

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​>25000

Find the value of NNN.

[5]
Markscheme

3 Unit A2 1: Pure Mathematics (A-level only) Questions

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