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.