SPM Practice Question 10 – 12

Question 10:
In a geometric progression, the first term is 27 and the fourth term is 1. Calculate
(a) the positive value of common ratio, r,
(b) the sum of the first n terms where n is sufficiently large till $r^n\approx 0$

Solution:

Question 11:
Express the recurring decimal 0.187187187 … as a fraction in its simplest form.

Solution:

Question 12:
$\begin{array}{l}\text{Given that }\frac{1}{p}=\mathrm{0.1666666.....}\\ =q+a+b+c+\mathrm{.....}\end{array}$
where p is a positive integer. If q = 0.1 and a + b + c are the first three terms of a geometric progression, state the value of a, b and c in decimal form. Hence find the value of p.

Solution: