Question 20

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Jambmaths question: 

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

Option A: 

3

Option B: 

5

Option C: 

$\sqrt{2}$

Option D: 

$\sqrt{5}$

Jamb Maths Solution: 

$\begin{align}  & \text{Common ratio}=r=\frac{2nd\text{ term}}{\text{1st term}} \\ & r=\frac{\sqrt{10}+2\sqrt{5}}{\sqrt{10}+\sqrt{5}}=\frac{(\sqrt{10}+2\sqrt{5})(\sqrt{10}-\sqrt{5})}{(\sqrt{10}+\sqrt{5})(\sqrt{10}-\sqrt{5})} \\ & r=\frac{10+2\sqrt{50}-\sqrt{50}-10}{10-5}=\frac{\sqrt{50}}{5}=\frac{5\sqrt{2}}{5} \\ & r=\sqrt{2} \\\end{align}$

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