Diagram \(n\) is formed with 52 sticks. Find the value of \(n\).

Find the total number of sticks used by Tomás for all 24 diagrams.

\(4 + 3(n - 1) = 52\)     (M1)(A1)

Note:     Award (M1) for substitution into the formula of the \(n\)th term of an arithmetic sequence, (A1) for correct substitution.

\(n = 17\)     (A1)     (C3)

[3 marks]

\(\frac{{24}}{2}(2 \times 4 + 23 \times 3)\)\(\,\,\,\)OR\(\,\,\,\)\(\frac{{24}}{2}(4 + 73)\)     (M1)(A1)(ft)

Notes:     Award (M1) for substitution into the sum of the first \(n\) terms of an arithmetic sequence formula, (A1)(ft) for their correct substitution, consistent with part (a).

924     (A1)(ft)     (C3)

Note:     Follow through from part (a).

[3 marks]