Question 6 - A-Level Maths

Exam Board	AQA
Module	C2 (Core Mathematics 2)
Year	2013
Session	January
Topic	Geometric Sequences and Series

A geometric series begins \(420 + 294 + 205.8 + \ldots\).
1. Show that the common ratio of the series is 0.7 .
2. Find the sum to infinity of the series.
3. Write the \(n\)th term of the series in the form \(p \times q ^ { n }\), where \(p\) and \(q\) are constants.
The first term of an arithmetic series is 240 and the common difference of the series is - 8 . The \(n\)th term of the series is \(u _ { n }\).
1. Write down an expression for \(u _ { n }\).
2. Given that \(u _ { k } = 0\), find the value of \(\sum _ { n = 1 } ^ { k } u _ { n }\).