Question 5 - A-Level Maths

Exam Board	AQA
Module	C2 (Core Mathematics 2)
Year	2010
Session	June
Topic	Geometric Sequences and Series

An infinite geometric series has common ratio \(r\).
The first term of the series is 10 and its sum to infinity is 50 .
1. Show that \(r = \frac { 4 } { 5 }\).
2. Find the second term of the series.
The first and second terms of the geometric series in part (a) have the same values as the 4th and 8th terms respectively of an arithmetic series.
1. Find the common difference of the arithmetic series.
2. The \(n\)th term of the arithmetic series is \(u _ { n }\). Find the value of \(\sum _ { n = 1 } ^ { 40 } u _ { n }\).