Write down the common difference of the sequence.

Calculate the sum of the first $50$ terms of the sequence.

${u_k}$ is the first term in the sequence which is negative.

Find the value of $k$.

$d = - 7$     (A1)     (C1)

[1 mark]

${S_{50}} = \frac{{50}}{2}(2(124) + 49( - 7))$     (M1)

Note: (M1) for correct substitution.

$= - 2375$     (A1)(ft)     (C2)

[2 marks]

$124 - 7(k - 1) < 0$     (M1)

$k > 18.7$ or $18.7$ seen     (A1)(ft)

$k = 19$     (A1)(ft)     (C3)

Note: (M1) for correct inequality or equation seen or for list of values seen or for use of trial and error.

[3 marks]

(a) Again, the omission of the negative sign was a too common fault.

This was generally well attempted.

The common misconception was confusion between $k$ and the value of the $k$^th term. Close reading of this part was required from the candidates.