Question 8 - A-Level Maths

Exam Board	CAIE
Module	P1 (Pure Mathematics 1)
Year	2015
Session	June
Topic	Geometric Sequences and Series

The first, second and last terms in an arithmetic progression are 56, 53 and -22 respectively. Find the sum of all the terms in the progression.
The first, second and third terms of a geometric progression are \(2 k + 6,2 k\) and \(k + 2\) respectively, where \(k\) is a positive constant.
1. Find the value of \(k\).
2. Find the sum to infinity of the progression.