Find ${u_1}$.

(i)     Given that ${u_n} = 516$ , find the value of n .

(ii)    For this value of n , find ${S_n}$ .

evidence of equation for ${u_{27}}$     M1

e.g. $263 = {u_1} + 26 \times 11$ , ${u_{27}} = {u_1} + (n - 1) \times 11$ , $263 - (11 \times 26)$

${u_1} = - 23$     A1     N1

[2 marks]

(i) correct equation     A1

e.g. $516 = - 23 + (n - 1) \times 11$ , $539 = (n - 1) \times 11$

$n = 50$     A1     N1

(ii) correct substitution into sum formula     A1

e.g. ${S_{50}} = \frac{{50( - 23 + 516)}}{2}$ , ${S_{50}} = \frac{{50(2 \times ( - 23) + 49 \times 11)}}{2}$

${S_{50}} = 12325$ (accept 12300)     A1     N1

[4 marks]

This problem was done well by the vast majority of candidates. Most students set out their working very neatly and logically and gained full marks.

This problem was done well by the vast majority of candidates. Most students set out their working very neatly and logically and gained full marks.