OCR C2 2012 June — Question 5

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2012
SessionJune
TopicArithmetic Sequences and Series

5
  1. A sequence \(u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots\) is defined by $$u _ { 1 } = 4 \quad \text { and } \quad u _ { n + 1 } = \frac { 2 } { u _ { n } } \quad \text { for } n \geqslant 1 .$$
    1. Write down the values of \(u _ { 2 }\) and \(u _ { 3 }\).
    2. Describe the behaviour of the sequence.
  2. In an arithmetic progression the ninth term is 18 and the sum of the first nine terms is 72. Find the first term and the common difference.