What is the common ratio of the G.P. (√10+√..

Question 1 Report

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

\sqrt{2}

√5

Answer Details

Common ratio r of the G.P is
$r = \frac{T_{n} + 1}{T_{n}} = \frac{T_{2}}{T_{1}}$
$r = \frac{\sqrt{10} + 2 \sqrt{5}}{\sqrt{10} + \sqrt{5}}$
$r = \frac{\sqrt{10} + 2 \sqrt{5}}{\sqrt{10} + \sqrt{5}} \times \frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} - \sqrt{5}}$
$= \frac{(\sqrt{10}) (\sqrt{10}) + (\sqrt{10}) (- \sqrt{5}) + (2 \sqrt{5}) (\sqrt{10}) + (2 \sqrt{5}) (- \sqrt{5})}{(\sqrt{10})^{2} - (\sqrt{5})^{2}}$
$\frac{10 - \sqrt{50} + 2 \sqrt{50} - 10}{10 - 5}$
$\frac{\sqrt{50}}{5}$
$\frac{\sqrt{25 \times 2}}{5}$
$\frac{5 \sqrt{2}}{5}$
$\sqrt{2}$

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Surds (radicals)

Sequence And Series

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What is the common ratio of the G.P. (√10+√5)+(√10+2√5)+... ( 10 + 5 ) + ( 10 + 2 5 ) + . . . ?

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