Question

If the numbers (x-2), (4x-1), (5x+2) are in A.P. find x.​

Answer 1

Answer :

x = 1

Step-by-step explanation :

Given,

• (x-2), (4x-1), (5x+2) are in A.P.

To find,

• the value of x

Solution,

⇒ In A.P., the difference between a term and the preceding term is constant.

⮞ If a , b and c are in A.P. , then

     b - a = c - b

     b + b = c + a

       2b = a + c

Let

• a = (x - 2)
• b = (4x - 1)
• c = (5x + 2)

Substitute,

   2(4x - 1) = (x - 2) + (5x + 2)

   8x - 2 = x - 2 + 5x + 2

   8x - 2 = 6x

   8x - 6x = 2

     2x = 2

     x = 2/2

     x = 1

The value of x is 1

Verification :

Put x = 1,

➙ x - 2 = 1 - 2 = -1

➙ 4x - 1 = 4(1) - 1 = 3

➙ 5x + 2 = 5(1) + 2 = 7

Let a₁ = -1

      a₂ = 3

      a₃ = 7

⇝ a₂ - a₁ = 3 - (-1) = 4

⇝ a₃ - a₂ = 7 - 3 = 4

➛ a₃ - a₂ = a₂ - a₁

The difference between a term and preceding term is constant.

Hence, they're in A.P.