What is the common ratio of the G.P. \(... | JAMB UTME - Mathematics - 2014

Question 1 Report

What is the common ratio of the G.P. \( (\sqrt{10}+\sqrt{5})+(\sqrt{10}+2\sqrt{5})+\ldots \)?

\sqrt{2}

√5

Answer Details

Common ratio r of the G.P is

r = \frac{T_{n} + 1}{T_{n}} = \frac{T_{2}}{T_{1}}

r = \frac{\sqrt{10} + 2 \sqrt{5}}{\sqrt{10} + \sqrt{5}}

r = \frac{\sqrt{10} + 2 \sqrt{5}}{\sqrt{10} + \sqrt{5}} \times \frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} - \sqrt{5}}

= \frac{(\sqrt{10}) (\sqrt{10}) + (\sqrt{10}) (- \sqrt{5}) + (2 \sqrt{5}) (\sqrt{10}) + (2 \sqrt{5}) (- \sqrt{5})}{(\sqrt{10})^{2} - (\sqrt{5})^{2}}

\frac{10 - \sqrt{50} + 2 \sqrt{50} - 10}{10 - 5}

\frac{\sqrt{50}}{5}

\frac{\sqrt{25 \times 2}}{5}

\frac{5 \sqrt{2}}{5}

\sqrt{2}

What is the common ratio of the G.P. \( (\sqrt{10}+\sqrt{5})+(\sqrt{10}+2\sqrt{5})+\ldots \)?