Find the common ratio of the sequence.

Find u₁, the first term of the sequence.

Calculate the sum of the first 10 terms of the sequence.

\(\frac{{101.25}}{{135}}\)     (M1)

\( = \frac{3}{4}(0.75)\)     (A1)     (C2)

\({u_1}{\left( {\frac{3}{4}} \right)^4} = 101.25\)     (M1)

OR

\({u_1}{\left( {\frac{3}{4}} \right)^3} = 135\)     (M1)

OR

(by list)

\({u_3} = 180,{\text{ }}{u_2} = 240\)     (M1)

Notes: Award (M1) for their correct substitution in geometric sequence formula, or stating explicitly \({u_3}\) and \({u_2}\).

\(({u_1} = )320\)     (A1)(ft)     (C2)

Note: Follow through from their answer to part (a).

\({S_{10}} = \frac{{320\left( {1 - {{\left( {\frac{3}{4}} \right)}^{10}}} \right)}}{{1 - \left( {\frac{3}{4}} \right)}}\)     (M1)

Notes: Award (M1) for their correct substitution in geometric series formula.

    Accept a list of all their ten geometric terms.

= 1210 (1207.918...)     (A1)(ft)     (C2)

Note: Follow through from their parts (a) and (b).

The weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question.

The weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question.

The weakest candidates erroneously used an arithmetic sequence rather than a geometric sequence as specified in the question.