OCR Mechanics 1 2018 March — Question 2

Exam BoardOCR
ModuleMechanics 1 (Mechanics 1)
Year2018
SessionMarch
TopicGeometric Sequences and Series

2 The first term of a geometric progression is 12 and the second term is 9 .
  1. Find the fifth term. The sum of the first \(N\) terms is denoted by \(S _ { N }\) and the sum to infinity is denoted by \(S _ { \infty }\). It is given that the difference between \(S _ { \infty }\) and \(S _ { N }\) is at most 0.0096 .
  2. Show that \(\left( \frac { 3 } { 4 } \right) ^ { N } \leqslant 0.0002\).
  3. Use logarithms to find the smallest possible value of \(N\).