If x+4, 6x-2 and 9x-4 are three consecutive terms of an arithmetic progression, then find x.a.2b.4c.6d.8
Question
If x+4, 6x-2 and 9x-4 are three consecutive terms of an arithmetic progression, then find x.
a. 2
b. 4
c. 6
d. 8
Solution
In an arithmetic progression, the difference between any two consecutive terms is constant. This is called the common difference.
Given that x+4, 6x-2 and 9x-4 are three consecutive terms of an arithmetic progression, we can set up the following equations based on the property of arithmetic progression:
The difference between the second and the first term is: (6x - 2) - (x + 4) = 5x - 6
The difference between the third and the second term is: (9x - 4) - (6x - 2) = 3x - 2
Since these differences are equal, we can set up the equation:
5x - 6 = 3x - 2
Solving this equation for x, we get:
5x - 3x = 6 + 2
2x = 8
x = 8 / 2
x = 4
So, the correct answer is b. 4.
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