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If $( x+2),\ 2x,\ ( 2x+4)$ are three consecutive terms of an A.P., find the value of $x$.
Given: $( x+2),\ 2x,\ ( 2x+4)$ are three consecutive terms of an A.P.
To do: To find the value of $x$.
Solution:
Given, $( x+2),\ 2x,\ ( 2x+4)$ are three consecutive terms of an A.P.
As known, if $a,\ b$ and $c$ are in A.P., then $b-a=c-b$.
Therefore, $2x-( x+2)=( 2x+4)-2x$
$\Rightarrow 2x-x-2=2x+4-2x$
$\Rightarrow x-2=4$
$\Rightarrow x=4+2$
$\Rightarrow x=6$
Thus, $x=6$.
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