Question

The second and fifth term of a geometrical progression are 3 and 1/81 respectively . Find the common ratio of the first term and the eight term.

Answer 1

$$b_2=b_1q, b_5=b_1q^4$$ $$\dfrac{b_5}{b_2}=\dfrac{b_1q^4}{b_1q}=q^3=\dfrac{\dfrac{1}{81}}{3}=\dfrac{1}{243}$$

$$q=\dfrac{\sqrt[3]{3}}{9}$$

$$\dfrac{b_1}{b_8}=\dfrac{b_1}{b_1q^7}=177147\sqrt[3]{9}$$