The first term of a geometric sequence is 200 and the sum of the first four terms is 324.8.

Find the common ratio.

The first term of a geometric sequence is 200 and the sum of the first four terms is 324.8.

Find the tenth term.

correct substitution into sum of a geometric sequence     (A1)

e.g. \(200\left( {\frac{{1 - {r^4}}}{{1 - r}}} \right)\) , \(200 + 200r + 200{r^2} + 200{r^3}\)

attempt to set up an equation involving a sum and 324.8     M1

e.g. \(200\left( {\frac{{1 - {r^4}}}{{1 - r}}} \right) = 324.8\) , \(200 + 200r + 200{r^2} + 200{r^3} = 324.8\)

\(r = 0.4\) (exact)     A2     N3

[4 marks]

correct substitution into formula     A1

e.g. \({u_{10}} = 200 \times {0.4^9}\)

\({u_{10}} = 0.0524288\) (exact), \(0.0524\)     A1     N1

[2 marks]

In part (a), although most candidates substituted correctly into the formula for the sum of a geometric series and set it equal to 324.8, some used the formula for the sum to infinity and a few the formula for the sum of an arithmetic series. The overwhelming error made was in attempting to solve the equation algebraically and getting nowhere, or getting a wrong answer. The great majority did not recognize the need to use the GDC to find the value of r.

In part (b) many did not obtain any marks since they weren't able to find an answer to part (a). Those who were able to get a value for r in part (a) generally went on to gain full marks in (b). However, this was one of the most common places for rounding errors to be made.