Additional Mathematics 0606: SEQUENCES AND SERIES Topical Past Paper Questions

A geometric progression has first term a and common ratio r, where a \ne 0, r > 0 and r \ne 1. The terms of the geometric progression are denoted by u_1, u_2, u_3, \ldots. (a) Given that $ u_{n+1} - u_n = \frac{1}{6}(u_{n+3} - u_{n+1}) $ show that $ r^2 + r - 6 = 0 $. [4] (b) It…

An arithmetic progression has first term $t$ and common difference 1.5. The 4th, 8th and 20th terms of this arithmetic progression form the 1st, 2nd and 3rd terms of a geometric progression. (a) Find the value of $t$. (b) Find the common ratio of the geometric progression.

(a) The first three terms of an arithmetic progression are $ \lg\theta^{2} $, $ \lg\theta^{5} $ and $ \lg\theta^{8} $. (i) Given that the sum to n terms of this progression is $ 4732\lg\theta $, find the value of n. (iii) This sum is equal to -14196. Find the exact value of $ \th…