Question

If 2x, x+10, 3x+2 are in AP, then x is equal to

Answer 1

AnsWer :

6.

Solution :

We have, AP.

Let First term be ' a '

and Common difference be ' d '

A/Q,

Let

• a = 2x
• b = x + 10
• c = 3x + 2

According to

$\tt Condition \begin{cases} \sf{When\: any \: given \:term}\\ \sf{ in\: under \: AP \: then,}\\ \sf{there \: common\: difference}\\ \sf{' d ' \: is \:equal.}\end{cases}$

$\tt \dagger \: \: \: \: \: b - a = c - a.$

$\tt\longmapsto ( x + 10 ) - ( 2x ) =( 3x + 2 ) - ( x + 10 )$

$\tt\longmapsto x + 10 - 2x = 3x + 2 - x - 10 .$

$\tt\longmapsto 10 - x =2x - 8$

$\tt\longmapsto 18 =3x .$

$\tt\longmapsto x = \dfrac{ \cancel{18}}{ \cancel3}$

$\tt\longmapsto x = 6.$

Therefore, the value of x is 6.