22M.1.SL.TZ2.2

pestleMathematicsAASLPaper 122M· sl-1-2-arithmetic-sequences-and-seriessource ↗

The $n$ ^th term of an arithmetic sequence is given by $u_{n} = 15 - 3 n$ .

State the value of the first term, $u_{1}$ .

[1]

Given that the $n$ ^th term of this sequence is $- 33$ , find the value of $n$ .

[2]

Find the common difference, $d$ .

[2]

Markscheme / solution

$u_{1} = 12$ A1

[1 mark]

$15 - 3 n = - 33$ (A1)

$n = 16$ A1

[2 marks]

valid approach to find $d$ (M1)

$u_{2} - u_{1} = 9 - 12$ OR recognize gradient is $- 3$ OR attempts to solve $- 33 = 12 + 15 d$

$d = - 3$ A1

[2 marks]

Examiners’ report

A large majority of candidates earned full marks for this question. In part (a), a surprising number of candidates did not substitute $n = 1$ into the given expression, erroneously stating $u_{1} = 15$ . Many of these candidates were able to earn follow-through marks in later parts of the question. In part (b), algebraic errors led a few candidates to find inappropriate values for $n$ , such as $n = - 6$ .

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