If x+4, 6x-2 and 9x-4 are three consecutive terms of an arithmetic progression, then find x.a.8b.4c.2d.6
Question
If x+4, 6x-2 and 9x-4 are three consecutive terms of an arithmetic progression, then find x.
a. 8
b. 4
c. 2
d. 6
Solution
In an arithmetic progression, the difference between any two consecutive terms is constant. This means that the difference between the second and first term is equal to the difference between the third and second term.
So, we can set up the following equation:
(6x - 2) - (x + 4) = (9x - 4) - (6x - 2)
Solving this equation will give us the value of x.
First, simplify both sides of the equation:
5x - 6 = 3x - 2
Then, subtract 3x from both sides:
2x - 6 = -2
Finally, add 6 to both sides:
2x = 4
Divide both sides by 2 to solve for x:
x = 2
So, the correct answer is c. 2.
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