Question

if 2x , x+1 and 3x-1 are in AP, the find value of x​

Answer 1

Step-by-step explanation:

see the attachment

hope it helped

Answer 2

SOLUTION

GIVEN

2x , x + 1 , 3x - 1 are in AP

TO DETERMINE

The value of x

EVALUATION

Here it is given that 2x , x + 1 , 3x - 1 are in AP

1st term = 2x

2nd term = x + 1

3rd term = 3x - 1

Since 2x , x + 1 , 3x - 1 are in AP

So there exists common difference

So we have

2nd term - 1st term = 3rd term - 2nd term

$\displaystyle \sf{ \implies (x + 1) - 2x = (3x - 1) - (x + 1)}$

$\displaystyle \sf{ \implies - x + 1 = 3x - 1- x - 1}$

$\displaystyle \sf{ \implies - x + 1 = 2 x - 2}$

$\displaystyle \sf{ \implies - x - 2 x = - 2 - 1}$

$\displaystyle \sf{ \implies - 3x = - 3}$

$\displaystyle \sf{ \implies x = 1}$

FINAL ANSWER

Hence the required value of x = 1

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