JAMB Mathematics 2014 Paper

Concept:In a geometric progression, the common ratio $r$ is obtained by dividing any term by the term immediately before it.Explanation:The first term is $T_1 = \sqrt{10} + \sqrt{5}$.The second term is $T_2 = \sqrt{10} + 2\sqrt{5}$.Therefore, $r = \frac{T_2}{T_1} = \frac{\sqrt{10} + 2\sqrt{5}}{\sqrt{10} + \sqrt{5}}$.Rationalise the denominator by multiplying both numerator and denominator by $\sqrt{10} - \sqrt{5}$:$$r = \frac{(\sqrt{10} + 2\sqrt{5})(\sqrt{10} - \sqrt{5})}{(\sqrt{10})^2 - (\sqrt{5})^2}$$Expanding the numerator gives:$$= \frac{10 - \sqrt{50} + 2\sqrt{50} - 10}{10 - 5}$$Simplify the numerator and denominator:$$= \frac{\sqrt{50}}{5} = \frac{5\sqrt{2}}{5} = \sqrt{2}$$Answer:The common ratio is $\sqrt{2}$, so the correct option is A.