First slide

Geometric progression

Question

$Value of y = (0.36)^{\log_{\frac{1}{4}} (\frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + \dots upto \infty)}$

Moderate

A

0.9
B

0.8
C

0.6
D

0.25

Solution

$\frac{1}{3} + \frac{1}{3^{2}} + \dots \infty = \frac{\frac{1}{3}}{1 - \frac{1}{3}} = \frac{1}{3} \times \frac{3}{2} = \frac{1}{2}$
$∴ y = (0.36)^{\log_{\frac{1}{4}} \frac{1}{2}} = {(0.36)}^{\frac{1}{2}} = 0.6$

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