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Binomial Expression

For what irra...

Question

For what irrational value of $x$ can three numbers, $0. (27), x$ and $0. (72)$ form a progression (arithmetic or geometric)? Find $x$ and the sum of four terms of the progression.

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Solution

For Arithmetic Progression
$2 x = .27 + .72$
$⟹ x = .495$
sum of four terms is $2.43$

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