Consider the infinite geometric sequence $3{\text{, }}3(0.9){\text{, }}3{(0.9)^2}{\text{, }}3{(0.9)^3}{\text{, }} \ldots$ .

Write down the 10th term of the sequence. Do not simplify your answer.

Consider the infinite geometric sequence $3{\text{, }}3(0.9){\text{, }}3{(0.9)^2}{\text{, }}3{(0.9)^3}{\text{, }} \ldots$ .

Find the sum of the infinite sequence.

${u_{10}} = 3{(0.9)^9}$    A1     N1

[1 mark]

recognizing $r = 0.9$     (A1)

correct substitution     A1

e.g.  $S = \frac{3}{{1 - 0.9}}$

$S = \frac{3}{{0.1}}$    (A1)

$S = 30$    A1     N3

[4 marks]

This question was well done by most candidates. There were a surprising number of candidates who lost a mark for not simplifying $\frac{3}{{0.1}}$ to 30 , and there were a few candidates who used the formula for the finite sum unsuccessfully.

This question was well done by most candidates. There were a surprising number of candidates who lost a mark for not simplifying $\frac{3}{{0.1}}$ to 30, and there were a few candidates who used the formula for the finite sum unsuccessfully.