X,4x+5 and 10x-5 are the first three terms of an arithmetic sequence. Determine the value of X.
you know that the difference between terms is constant, so
(4x+5)-(x) = (10x-5)-(4x+5)
now just solve for x.
x=5
To determine the value of X in the given arithmetic sequence, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
Here, a1 represents the first term, d represents the common difference, and an represents the nth term.
Given the three terms as X, 4X + 5, and 10X - 5, we can set up two equations using the formula:
4X + 5 = X + (2-1)d (Equation 1)
10X - 5 = X + (3-1)d (Equation 2)
Simplifying Equation 1:
4X + 5 = X + d
Simplifying Equation 2:
10X - 5 = X + 2d
Next, we need to eliminate the variable d from the equations. We can do this by subtracting Equation 1 from Equation 2:
10X - 5 - (4X + 5) = X + 2d - (X + d)
Simplifying the equation:
6X - 10 = X + d
Now, we can substitute the value of d from Equation 1 into this equation:
6X - 10 = X + (4X + 5)
Simplifying further:
6X - 10 = X + 4X + 5
Combine like terms:
6X - 10 = 5X + 5
Subtract 5X from both sides:
X - 10 = 5
Add 10 to both sides:
X = 15
Therefore, the value of X in the given arithmetic sequence is 15.