Question 3 - A-Level Maths

Exam Board	Edexcel
Module	C1 (Core Mathematics 1)
Topic	Arithmetic Sequences and Series

The first three terms of an arithmetic series are \(p , 5 p - 8\), and \(3 p + 8\) respectively.
1. Show that \(p = 4\).
2. Find the value of the 40th term of this series.
3. \(\mathrm { f } ( x ) = x ^ { 2 } - k x + 9\), where \(k\) is a constant.
4. Find the set of values of \(k\) for which the equation \(\mathrm { f } ( x ) = 0\) has no real solutions.
Given that \(k = 4\),
express \(\mathrm { f } ( x )\) in the form \(( x - p ) ^ { 2 } + q\), where \(p\) and \(q\) are constants to be found,