| Exam Board | Edexcel |
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| Module | PMT Mocks (PMT Mocks) |
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| Topic | Geometric Sequences and Series |
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15. The first three terms of a geometric series where \(\theta\) is a constant are
$$- 8 \sin \theta , \quad 3 - 2 \cos \theta \quad \text { and } \quad 4 \cot \theta$$
a. Show that \(4 \cos ^ { 2 } \theta + 20 \cos \theta + 9 = 0\)
Given that \(\theta\) lies in the interval \(90 ^ { \circ } < \theta < 180 ^ { \circ }\),
b. Find the value of \(\theta\).
c. Hence prove that this series is convergent.
d. Find \(S _ { \infty }\), in the form \(a ( 1 - \sqrt { 3 } )\)