Write down the common ratio of the sequence.

Find the value of \({u_5}\).

Find the smallest value of \(n\) for which \({u_n}\) is less than \({10^{ - 3}}\).

\(\frac{1}{2}{\text{ }}(0.5)\)     (A1)     (C1)

[1 mark]

\(18 \times {\left( {\frac{1}{2}} \right)^4}\)     (M1)

Note:     Award (M1) for their correct substitution into the geometric sequence formula. Accept a list of their five correct terms.

\(1.125{\text{ }}\left( {1.13,{\text{ }}\frac{9}{8}} \right)\)     (A1)(ft)     (C2)

Note:     Follow through from their common ratio from part (a).

[2 marks]

\(18 \times {\left( {\frac{1}{2}} \right)^{n - 1}} < {10^{ - 3}}\)     (M1)(M1)

Notes:     Award (M1) for their correct substitution into the geometric sequence formula with a variable in the exponent, (M1) for comparing their expression with \({10^{ - 3}}{\text{ }}\left( {\frac{1}{{1000}}} \right)\).

Accept an equation.

\(n = 16\)     (A1)(ft)     (C3)

Note:     Follow through from their common ratio from part (a). “\(n\)” must be a positive integer for the (A1) to be awarded.

[3 marks]