Question on: JAMB Mathematics - 2024
What is the common ratio of the G.P. \((\sqrt{10} + \sqrt{5}) + (\sqrt{10} + 2\sqrt{5}) + ...\)?
A
\(\sqrt{2}\)
B
\(\sqrt{5}\)
C
3
D
5
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Correct Option: A
The common ratio \( r \) of a G.P. is the ratio of the second term to the first term:
\[ r = \frac{\sqrt{10} + 2\sqrt{5}}{\sqrt{10} + \sqrt{5}} \]
Rationalize by multiplying numerator and denominator by \( \sqrt{10} - \sqrt{5} \):
\[ r = \frac{(\sqrt{10} + 2\sqrt{5})(\sqrt{10} - \sqrt{5})}{(\sqrt{10} + \sqrt{5})(\sqrt{10} - \sqrt{5})} = \frac{\sqrt{50}}{5} = \sqrt{2} \]
The common ratio is \( \sqrt{2} \).
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