| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2009 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Recursive sequence definition |
| Difficulty | Moderate -0.8 This is a straightforward geometric sequence question requiring basic recall and application of standard formulas. Part (i) involves simple recursive calculation and identification of sequence type. Part (ii) requires checking |r| < 1 and applying the sum to infinity formula S = a/(1-r), both routine procedures for C2 level with no problem-solving insight needed. |
| Spec | 1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
8 The terms of a sequence are given by
$$\begin{aligned}
u _ { 1 } & = 192 \\
u _ { n + 1 } & = - \frac { 1 } { 2 } u _ { n }
\end{aligned}$$
(i) Find the third term of this sequence and state what type of sequence it is.\\
(ii) Show that the series $u _ { 1 } + u _ { 2 } + u _ { 3 } + \ldots$ converges and find its sum to infinity.
\hfill \mbox{\textit{OCR MEI C2 2009 Q8 [5]}}