In a geometric sequence, the fourth term is 8 times the first term. The sum of the first 10 terms is 2557.5. Find the 10th term of this sequence.

correct equation to find \(r\)     (A1)

eg\(\,\,\,\,\,\)\({u_1}{r^3} = 8{u_1},{\text{ }}{r^3} = 8\)

\(r = 2\) (seen anywhere)     (A1)

correct equation to find \({u_1}\)     A1

eg\(\,\,\,\,\,\)\({u_1}({2^{10}} - 1) = 2557.5,{\text{ }}{u_1} = \frac{{2557.5}}{{{r^{10}} - 1}}(r - 1)\)

\({u_1} = 2.5\)    (A1)

\({u_{10}} = 2.5{(2)^9}\)    (M1)

1280     A1     N4

[6 marks]

The majority of candidates did well on this question although identifying the common ratio was not always as easily done and some candidates lost marks as a result of using an inappropriate method such as 8/4. Other candidates correctly guessed the value of \(r\) or did so by showing that if \(r = 2\), then the ratio of the fourth term to the first term would be 8. It was also disappointing to see some candidates use an incorrect formula for the sum of the first \(n\) terms of a geometric series: a common error seen was \(2557.5 = \frac{{{u_1}({2^{10}} - 1)}}{{10 - 1}}\), which led to the wrong answer of 22.5.