(a)     Write down the value of $d$ .

(b)     Find

  (i)      ${u_{100}}$ ;

  (ii)      ${S_{100}}$ .

(c)     Given that ${u_n} = 1502$ , find the value of $n$ .

Write down the value of $d$ .

Find

  (i)      ${u_{100}}$ ;

  (ii)      ${S_{100}}$ .

Given that ${u_n} = 1502$ , find the value of $n$ .

(a)     $d = 3$     A1     N1

[1 mark]

(b)     (i)     correct substitution into term formula     (A1)

e.g. ${u_{100}} = 5 + 3(99)$ , $5 + 3(100 - 1)$

${u_{100}} = 302$     A1     N2

(ii)     correct substitution into sum formula     (A1)

eg   ${S_{100}} = \frac{{100}}{2}(2(5) + 99(3))$ , ${S_{100}} = \frac{{100}}{2}(5 + 302)$

${S_{100}} = 15350$     A1     N2

[4 marks]

(c)     correct substitution into term formula     (A1)

eg     $1502 = 5 + 3(n - 1)$ ,  $1502 = 3n + 2$

$n = 500$     A1     N2

[2 marks]

Total [7 marks]

$d = 3$     A1     N1

[1 mark]

(i)     correct substitution into term formula     (A1)

e.g. ${u_{100}} = 5 + 3(99)$ , $5 + 3(100 - 1)$

${u_{100}} = 302$     A1     N2

(ii)     correct substitution into sum formula     (A1)

eg   ${S_{100}} = \frac{{100}}{2}(2(5) + 99(3))$ , ${S_{100}} = \frac{{100}}{2}(5 + 302)$

${S_{100}} = 15350$     A1     N2

[4 marks]

correct substitution into term formula     (A1)

eg     $1502 = 5 + 3(n - 1)$ ,  $1502 = 3n + 2$

$n = 500$     A1     N2

[2 marks]

Total [7 marks]

The majority of candidates had little difficulty with this question. If errors were made, they were normally made out of carelessness. A very few candidates mistakenly used the formulas for geometric sequences and series.

The majority of candidates had little difficulty with this question. If errors were made, they were normally made out of carelessness. A very few candidates mistakenly used the formulas for geometric sequences and series.

The majority of candidates had little difficulty with this question. If errors were made, they were normally made out of carelessness. A very few candidates mistakenly used the formulas for geometric sequences and series.

The majority of candidates had little difficulty with this question. If errors were made, they were normally made out of carelessness. A very few candidates mistakenly used the formulas for geometric sequences and series.