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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Updated on: 10-Oct-2022

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