The terms 4x + 36, 2x - 6, and 3x - 27 are consecutive terms in an arithmetic sequence. What is the value of x ?
since the difference is constant,
(2x-6) - (4x+36) = (3x-27) - (2x-6)
now just solve for x
2x-6-4x-36=3x-27-2x-6
2x-4x-3x+2x=-27-6+36
-5x=3
x=-3
x=-3_5
To determine the value of x, we need to find the common difference of the arithmetic sequence first.
The common difference (d) between consecutive terms of an arithmetic sequence is obtained by subtracting any two consecutive terms. In this case, we can subtract the second term (2x - 6) from the first term (4x + 36) to find the common difference:
Common Difference (d) = (4x + 36) - (2x - 6)
= 4x + 36 - 2x + 6
= 2x + 42
Now that we know the common difference (2x + 42), we can set up another equation using the third term (3x - 27) and the common difference:
Third term = First term + 2 * Common Difference
Substituting the values, we have:
(3x - 27) = (4x + 36) + 2 * (2x + 42)
Now, let's solve for x:
3x - 27 = 4x + 36 + 4x + 84
3x - 27 = 8x + 120
Bringing like terms together:
3x - 8x = 120 + 27
-5x = 147
Dividing both sides of the equation by -5:
x = 147 / -5
x = -29.4
Therefore, the value of x is -29.4.