CAIE P1 2020 November — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2020
SessionNovember
TopicArithmetic Sequences and Series

7 The first and second terms of an arithmetic progression are \(\frac { 1 } { \cos ^ { 2 } \theta }\) and \(- \frac { \tan ^ { 2 } \theta } { \cos ^ { 2 } \theta }\), respectively, where \(0 < \theta < \frac { 1 } { 2 } \pi\).
  1. Show that the common difference is \(- \frac { 1 } { \cos ^ { 4 } \theta }\).
  2. Find the exact value of the 13th term when \(\theta = \frac { 1 } { 6 } \pi\).