9709 P11 - Nov 2009 - Q8
808
The first term of an arithmetic progression is 8 and the common difference is \(d\), where \(d \neq 0\). The first term, the fifth term and the eighth term of this arithmetic progression are the first term, the second term and the third term, respectively, of a geometric progression whose common ratio is \(r\).
(i) Write down two equations connecting \(d\) and \(r\). Hence show that \(r = \frac{3}{4}\) and find the value of \(d\). [6]
(ii) Find the sum to infinity of the geometric progression. [2]
(iii) Find the sum of the first 8 terms of the arithmetic progression. [2]
