Q165 / 270 · NDA 2012 (Phase 1) · Mathematics

What does the series $1+3^{-\frac{1}{2}}+3+\frac{1}{3 \sqrt{3}}+\ldots$ represent?

  • A
    AP
  • B
    GP
  • C
    HP
  • Correct answer
    D
    None of the above

Solution

$\begin{aligned} & 1+\frac{1}{\sqrt{3}}+3+\frac{1}{3 \sqrt{3}}+\ldots \\ & \frac{a_2}{a_1}=\frac{1}{\sqrt{3}} \\ & \frac{a_3}{a_2}=\frac{3}{1 / \sqrt{3}} \\ & \frac{a_4}{a_3}=\frac{1 / 3 \sqrt{3}}{3} .\end{aligned}$

Hence, the correct answer is option: 'D'.

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