Edexcel C2 2008 June — Question 6

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2008
SessionJune
TopicGeometric Sequences and Series

6. A geometric series has first term 5 and common ratio \(\frac { 4 } { 5 }\). Calculate
  1. the 20th term of the series, to 3 decimal places,
  2. the sum to infinity of the series. Given that the sum to \(k\) terms of the series is greater than 24.95,
  3. show that \(k > \frac { \log 0.002 } { \log 0.8 }\),
  4. find the smallest possible value of \(k\).