What Should Be The Value Of X So That X +2, 3x-2, 7x-12 Will Form An Arithmetic Sequence? Justify Your Answer.

what should be the value of x so that x +2, 3x-2, 7x-12 will form an arithmetic sequence? justify your answer.

 

Answer:

x = 3

Step-by-step explanation:

Use the common difference (d) formula:

d = a₂-a₁ =a₃ - a₂

Where:

a₁ = x+2

a₂ = 3x-2

a₃ = 7x-12

Equation:

(3x-2) - (x + 2) = (7x - 12) - (3x - 2)

3x - 2 - x - 2 = 7x - 12 - 3x + 2

Combine the like terms:

3x - x - 7x + 3x = 2 + 2 - 12 + 2

-2x = -6

-2x/-2 = -6/-2

x = 3

Substitute 3 to x:

a₁ = x+2  ⇒ (3)=2 = 5

a₂ = 3x-2  ⇒  3(3)-2 = 7

a₃ = 7x-12  ⇒  7(3)-12 = 9

Write the sequence after substituting x=3:

The sequence is 5, 7, 9.

Where the common difference is 2.