In the arithmetic series with ${n^{{\text{th}}}}$ term ${u_n}$ , it is given that ${u_4} = 7$ and ${u_9} = 22$ .

Find the minimum value of n so that ${u_1} + {u_2} + {u_3} + ... + {u_n} > 10\,000$ .

${u_4} = {u_1} + 3d = 7$ , ${u_9} = {u_1} + 8d = 22$     A1A1

Note: 5d = 15 gains both above marks

${u_1} = - 2$ , $d = 3$     A1

${S_n} = \frac{n}{2}\left( { - 4 + (n - 1)3} \right) > 10\,000$     M1

$n = 83$     A1

[5 marks]

This question was well answered by most candidates. A few did not realise that the answer had to be an integer.