19N.1.SL.TZ0.S_1

pestleMathematicsAASLPaper 119N· sl-1-2-arithmetic-sequences-and-seriessource ↗

In an arithmetic sequence, ${u_2} = 5$ and ${u_3} = 11$ .

Find the common difference.

[2]

Find the first term.

[2]

Find the sum of the first $20$ terms.

[2]

Markscheme / solution

valid approach (M1)

eg $11 - 5$ , $11 = 5 + d$

$d = 6$ A1 N2

[2 marks]

valid approach (M1)

eg ${u_2} - d$ , $5 - 6$ , ${u_1} + \left( {3 - 1} \right)\left( 6 \right) = 11$

${u_1} = - 1$ A1 N2

[2 marks]

correct substitution into sum formula

eg $\frac{{20}}{2}\left( {2\left( { - 1} \right) + 19\left( 6 \right)} \right)$ , $\frac{{20}}{2}\left( { - 1 + 113} \right)$ (A1)

${S_{20}} = 1120$ A1 N2

[2 marks]

Examiners’ report

[N/A]