In an arithmetic sequence, ${S_{40}} = 1900$ and ${u_{40}} = 106$ . Find the value of ${u_1}$ and of d .

METHOD 1

substituting into formula for ${S_{40}}$     (M1)

correct substitution     A1

e.g. $1900 = \frac{{40({u_1} + 106)}}{2}$

${u_1} = - 11$    A1     N2

substituting into formula for ${u_{40}}$ or ${S_{40}}$     (M1)

correct substitution     A1

e.g. $106 = - 11 + 39d$ , $1900 = 20( - 22 + 39d)$

$d = 3$     A1     N2

METHOD 2

substituting into formula for ${S_{40}}$     (M1)

correct substitution     A1

e.g. $20(2{u_1} + 39d) = 1900$

substituting into formula for ${u_{40}}$     (M1)

correct substitution     A1

e.g. $106 = {u_1} + 39d$

${u_1} = - 11$ , $d = 3$     A1A1     N2N2

[6 marks]

Most candidates answered this question correctly. Those who chose to solve with a system of equations often did so algebraically, using a fair bit of time doing so and sometimes making a careless error in the process. Few candidates took advantage of the system solving features of the GDC.