Find the common ratio.

Find the 10th term.

Find the exact sum of the infinite sequence.

evidence of dividing two terms     (M1)

e.g. $- \frac{{1800}}{{3000}}$ , $- \frac{{1800}}{{1080}}$

$r = - 0.6$     A1     N2

[2 marks]

evidence of substituting into the formula for the 10th term     (M1)

e.g. ${u_{10}} = 3000{( - 0.6)^9}$

${u_{10}} = 30.2$ (accept the exact value $- 30.233088$)     A1     N2

[2 marks]

evidence of substituting into the formula for the infinite sum     (M1)

e.g. $S = \frac{{3000}}{{1.6}}$

$S = 1875$     A1     N2

[2 marks]

This question was generally well done by most candidates.

This question was generally well done by most candidates, although quite a few showed difficulty answering part (b) exactly or to three significant figures.

This question was generally well done by most candidates, although quite a few showed difficulty answering part (b) exactly or to three significant figures. Some candidates reversed the division of terms to obtain a ratio of $- \frac{5}{3}$. Of these, most did not recognize this ratio as an inappropriate value when finding the sum in part (c).