First slide

Geometric progression

Question

$If (1 - p) (1 + 2 x + 4 x^{2} + 8 x^{3} + 16 x^{4} + 32 x^{5}) = 1 - p^{6} \cdot p \neq 1 then a value of \frac{p}{x} is$

Moderate

A

$\frac{1}{2}$
B

2
C

$\frac{1}{4}$
D

4

Solution

$\frac{(1 - 2 x) (1 + 2 x + 4 x^{2} + 8 x^{3} + 16 x^{4} + 32 x^{5})}{1 - 2 x} = \frac{1 - p^{6}}{(1 - p)}$
$\frac{1 - (2 x)^{6}}{1 - 2 x} = \frac{1 - p^{6}}{1 - p} \Rightarrow p = 2 x$
$\Rightarrow \frac{p}{x} = 2$

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