AQA C2 2007 June — Question 2

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2007
SessionJune
TopicGeometric Sequences and Series

2 The \(n\)th term of a geometric sequence is \(u _ { n }\), where $$u _ { n } = 3 \times 4 ^ { n }$$
  1. Find the value of \(u _ { 1 }\) and show that \(u _ { 2 } = 48\).
  2. Write down the common ratio of the geometric sequence.
    1. Show that the sum of the first 12 terms of the geometric sequence is \(4 ^ { k } - 4\), where \(k\) is an integer.
    2. Hence find the value of \(\sum _ { n = 2 } ^ { 12 } u _ { n }\).