Question

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If the numbers x-2, 4x-1 and 5x-2 are in A.P., find the value of x.​

Answer 1

Answer:

Common difference cannot be changed. So common in x - 2 , 4x - 1 and 5x + 2 will be same.

Difference between 5x + 2 and 4x - 1 = 5x + 2 - ( 4x - 1 ) = 5x - 4x + 2 + 1 = x + 3

Difference between 4x - 1 and x - 2 = 4x - 1 - ( x - 2 ) = 4x - x - 1 + 2 = 3x + 1

As we know that they common difference will be same.

Difference between 5x + 2 and 4x - 1 = Difference between 4x - 1 and x - 2

x + 3 = 3x + 1

3 - 1 = 3x - x

2 = 2x

1 = x

Therefore, value of x satisfying the equation is 1.