21M.1.SL.TZ1.3

pestleMathematicsAASLPaper 121M· sl-1-2-arithmetic-sequences-and-seriessource ↗

Consider an arithmetic sequence where $u_{8} = S_{8} = 8$ . Find the value of the first term, $u_{1}$ , and the value of the common difference, $d$ .

Markscheme / solution

METHOD 1 (finding $u_{1}$ first, from $S_{8}$ )

$4 (u_{1} + 8) = 8$ (A1)

$u_{1} = - 6$ A1

$u_{1} + 7 d = 8$ OR $4 (2 u_{1} + 7 d) = 8$ (may be seen with their value of $u_{1}$ ) (A1)

attempt to substitute their $u_{1}$ (M1)

$d = 2$ A1

METHOD 2 (solving simultaneously)

$u_{1} + 7 d = 8$ (A1)

$4 (u_{1} + 8) = 8$ OR $4 (2 u_{1} + 7 d) = 8$ OR $u_{1} = - 3 d$ (A1)

attempt to solve linear or simultaneous equations (M1)

$u_{1} = - 6, d = 2$ A1A1

[5 marks]

Examiners’ report

[N/A]