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

$\sqrt{2}$

$\sqrt{5}$

Correct answer is A

Common ratio r of the G.P is

$r = \frac{T_n + 1}{T_n} = \frac{T_2}{T_1}$

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

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

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

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

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

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

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

$\sqrt{2}$

See all Mathematics questions & answers

See more JAMB questions & answers

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

Similar Questions

Aptitude Tests

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

Similar Questions

Aptitude Tests

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