Question 8 - A-Level Maths

Exam Board	CAIE
Module	P1 (Pure Mathematics 1)
Year	2018
Session	June
Topic	Geometric Sequences and Series

A geometric progression has a second term of 12 and a sum to infinity of 54 . Find the possible values of the first term of the progression.
The \(n\)th term of a progression is \(p + q n\), where \(p\) and \(q\) are constants, and \(S _ { n }\) is the sum of the first \(n\) terms.
1. Find an expression, in terms of \(p , q\) and \(n\), for \(S _ { n }\).
2. Given that \(S _ { 4 } = 40\) and \(S _ { 6 } = 72\), find the values of \(p\) and \(q\).