OCR MEI C2 2009 January — Question 8

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2009
SessionJanuary
TopicGeometric Sequences and Series

8 The terms of a sequence are given by $$\begin{aligned} u _ { 1 } & = 192
u _ { n + 1 } & = - \frac { 1 } { 2 } u _ { n } \end{aligned}$$
  1. Find the third term of this sequence and state what type of sequence it is.
  2. Show that the series \(u _ { 1 } + u _ { 2 } + u _ { 3 } + \ldots\) converges and find its sum to infinity.