Mathematics: SEQUENCES - SERIES Topical Past Paper Questions

An infinite geometric series has first term $ u_{1}=a $ and second term $ u_{2}=\frac{1}{4}a^{2}-3a $, where a>0. (a) Find the common ratio in terms of a. [2] (b) Find the values of a for which the sum to infinity of the series exists. [3] (c) Find the value of a when $ S_{\infty…

## [Maximum mark: 7] The first two terms of a geometric sequence are $ u_{1}=2.1 $ and $ u_{2}=2.226 $. (a) Find the value of r. (b) Find the value of $ u_{10} $. (c) Find the least value of n such that $ S_{n} > 5543 $.

[Maximum mark: 6] The sum of an infinite geometric sequence is 33.25. The second term of the sequence is 7.98. Find the possible values of r.