The first three terms of an arithmetic progression are \(25,4 p - 1\) and \(13 - p\), where \(p\) is a constant. Find the value of the tenth term of the progression.
The first three terms of a geometric progression are \(25,4 q - 1\) and \(13 - q\), where \(q\) is a positive constant.
Find the sum to infinity of the progression.
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The diagram shows part of the curve with equation \(y = \frac { 1 } { ( 5 x - 4 ) ^ { \frac { 1 } { 3 } } }\) and the lines \(x = 2.4\) and \(y = 1\). The curve intersects the line \(y = 1\) at the point \(( 1,1 )\).
Find the exact volume of the solid generated when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.