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.