To solve this problem, we need to determine the value of x, which represents the fifth term of the arithmetic sequence.
Let's break down the information given:
Sum of the first four terms: $10
Fifth term: X$
Sixth term: $6
We can set up the equation as follows:
(first term + second term + third term + fourth term) + Fifth term + Sixth term = Sum of the first four terms + Fifth term + Sixth term
Let's represent the first term as a, and the common difference as d:
(a + (a + d) + (a + 2d) + (a + 3d)) + X$ + $6 = $10 + X$ + $6
4a + 6d + X$ + $6 = $16 + X$
Since we know the sixth term is 6, we can also represent the sixth term in terms of a and d:
a + 5d = $6
Now we have a system of equations:
4a + 6d + X$ + $6 = $16 + X$
a + 5d = $6
Let's solve this system of equations to find the value of x:
From the second equation, we can express a in terms of d:
a = $6 - 5d
Substituting this expression for a in the first equation:
4($6 - 5d) + 6d + X$ + $6 = $16 + X$
Simplifying:
24 - 20d + 6d + X$ + $6 = $16 + X$
-14d + X$ + $30 = $16 + X$
Subtracting X$ from both sides:
-14d + $30 = $16
Subtracting $16 from both sides:
-14d = -$14
Dividing both sides by -14:
d = 1
Now that we know the common difference d is 1, we can substitute it back into the second equation to find a:
a + 5(1) = $6
a + 5 = $6
Subtracting 5 from both sides:
a = $1
Finally, substitute a and d into the equation for the fifth term:
a + 4d = X$
$1 + 4(1) = X$
$1 + 4 = X$
X = $5
The value of x is $5.
The answer is: 5
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
The sum of the first four terms of an arithmetic sequence is $10$. If the fifth term is X$, The sixth term is 6. What is the value of unknown variable X?

### Answer:
