(a) A sequence has terms \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) defined by \(u _ { 1 } = 3\) and \(u _ { n + 1 } = u _ { n } ^ { 2 } - 5\) for \(n \geqslant 1\).
Find the values of \(u _ { 2 } , u _ { 3 }\) and \(u _ { 4 }\).
Describe the behaviour of the sequence.
(b) The second, third and fourth terms of a geometric progression are 12,8 and \(\frac { 16 } { 3 }\). Determine the sum to infinity of this geometric progression. [0pt]
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In this question you must show detailed reasoning.
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The diagram shows the cuboid \(A B C D E F G H\) where \(A D = 3 \mathrm {~cm} , A F = ( 2 x + 1 ) \mathrm { cm }\) and \(D C = ( x - 2 ) \mathrm { cm }\).
The volume of the cuboid is at most \(9 \mathrm {~cm} ^ { 3 }\).
Find the range of possible values of \(x\). Give your answer in interval notation. [0pt]
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