Edexcel C12 2016 October — Question 6

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2016
SessionOctober
TopicGeometric Sequences and Series

6. A sequence is defined by $$\begin{aligned} u _ { 1 } & = 36
u _ { n + 1 } & = \frac { 2 } { 3 } u _ { n } , \quad n \geqslant 1 \end{aligned}$$
  1. Find the exact simplified values of \(u _ { 2 } , u _ { 3 }\) and \(u _ { 4 }\)
  2. Write down the common ratio of the sequence.
  3. Find, giving your answer to 4 significant figures, the value of \(u _ { 11 }\)
  4. Find the exact value of \(\sum _ { i = 1 } ^ { 6 } u _ { i }\)
  5. Find the value of \(\sum _ { i = 1 } ^ { \infty } u _ { i }\)