Consider the arithmetic sequence $2{\text{, }}5{\text{, }}8{\text{, }}11{\text{,}} \ldots$ .

Find ${u_{101}}$ .

Consider the arithmetic sequence $2{\text{, }}5{\text{, }}8{\text{, }}11{\text{,}} \ldots$ .

Find the value of n so that ${u_n} = 152$ .

$d = 3$     (A1)

evidence of substitution into ${u_n} = a + (n - 1)d$     (M1)

e.g. ${u_{101}} = 2 + 100 \times 3$

${u_{101}} = 302$     A1     N3

[3 marks]

correct approach     (M1)

e.g. $152 = 2 + (n - 1) \times 3$

correct simplification     (A1)

e.g. $150 = (n - 1) \times 3$ , $50 = n - 1$ , $152 = - 1 + 3n$

$n = 51$     A1     N2

[3 marks]

Candidates probably had the most success with this question with many good solutions which were written with the working clearly shown. Many used the alternate approach of ${u_n} = 3n - 1$ .

Candidates probably had the most success with this question with many good solutions which were written with the working clearly shown. Many used the alternate approach of ${u_n} = 3n - 1$ .