First slide

Geometric progression

Question

If there successive terms of a G.P with common ratio r(r>1) form the sides of a $Δ A B C$ and [r] denotes greates integer function, then $[r] + [- r] =$

Moderate

A

0
B

1
C

-1
D

$- \frac{1}{2}$

Solution

$a, a r, a r^{2} are sides of a triangle \Rightarrow a r^{2} - a r < a$
$\begin{array}{l} \Rightarrow r^{2} - r < 1 \Rightarrow r^{2} - r - 1 < 0 \\ r = \frac{\sqrt{5} + 1}{2} = \frac{2.14 + 1}{2} \Rightarrow r = 1.57 \\ \Rightarrow [r] = 1, [- r] = - 2 \Rightarrow [r] + [- r] = - 1 \end{array}$

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