R D Sharma Solutions for Chapter: Geometric Progressions, Exercise 4: EXERCISE 20.4

Find the sum of the terms of an infinite decreasing $\mathrm{G}.\mathrm{P}.$ in which all the terms are positive, the first term is $4$, and the difference between the third and fifth term is equal to $\frac{32}{81}$.

Express the recurring decimal $0.125125125...$ as a rational number. If the answer is $\frac{125}{p}$, find the value of $p$.

Find the rational number whose decimal expansion is $0.4\stackrel{-}{23}$.

Find the rational numbers having the following decimal expansions:

$0.\stackrel{-}{3}$

Find the rational numbers having the following decimal expansions:

$0.\overline{231}$

Find the rational numbers having the following decimal expansions:

$3.5\stackrel{-}{2}$

Find the rational numbers having the following decimal expansion:

$0.6\stackrel{-}{8}$

One side of an equilateral triangle is $18 \mathrm{c}\mathrm{m}$. The mid-points of its sides are joined to form another triangle whose mid-points, in turn, are joined to form still another triangle. The process is continued indefinitely. Find the sum of the perimeters of all the triangles. (Give your answer in centimetres)