Home » What is the common ratio of the G.P. ((sqrt{10} + sqrt{5}) + (sqrt{10} + 2sqrt{5})…

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

What is the common ratio of the G.P. ((sqrt{10} + sqrt{5}) + (sqrt{10} + 2sqrt{5}) + … )?
  • A.
    (sqrt{2})
  • B.
    (sqrt{5})
  • C.
    3
  • D.
    5
Correct Answer: Option A
Explanation

Common ratio r of the G.P is
(r = frac{T_n + 1}{T_n} = frac{T_2}{T_1})
(r = frac{sqrt{10} + 2sqrt{5}}{sqrt{10} + sqrt{5}})
(r = frac{sqrt{10} + 2sqrt{5}}{sqrt{10} + sqrt{5}} times frac{sqrt{10} – sqrt{5}}{sqrt{10} – sqrt{5}} )
( = frac{(sqrt{10})(sqrt{10}) + (sqrt{10})(-sqrt{5}) + (2sqrt{5})(sqrt{10}) + (2sqrt{5})(-sqrt{5})}{(sqrt{10})^2 – (sqrt{5})^2})
(frac{10 – sqrt{50} + 2sqrt{50} – 10}{10 – 5})
(frac{sqrt{50}}{5})
(frac{sqrt{25 times 2}}{5})
(frac{5sqrt{2}}{5})
(sqrt{2})

There is an explanation video available below.

Explanation Video

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