(i) Find the common difference.

(ii) Find the first term of the sequence.

Calculate the eighty-fourth term.

Calculate the sum of the first 200 terms.

(i) $u_5 = u_1 + 4d = 20$

$u_{12} = u_1 + 11d = 41$     (M1)

(M1) for both equations correct (or (M1) for $20 + 7d = 41$)

$7d = 21$

$d = 3$     (A1)     (C2)

(ii) $u_1 + 12 = 20$

$u_1 = 8$     (A1)(ft)     (C1)

[3 marks]

$u_{84} = 8 + (84 - 1)3$

$= 257$     (A1)(ft)     (C1)

[1 mark]

$S_{200} = 100(16 + 199 \times 3)$     (M1)

$= 61300$     (A1)(ft)     (C2)

[2 marks]

This question was generally answered well. Most of the candidates had a good understanding of how to use the formulae for an arithmetic sequence.

This question was generally answered well. Most of the candidates had a good understanding of how to use the formulae for an arithmetic sequence.

This question was generally answered well. Most of the candidates had a good understanding of how to use the formulae for an arithmetic sequence.