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Possible Answer
Let d be the common difference. Then, y = x + d, z = x + 2d, and w = x + 3d. Substitute these values into the expression x + w - y and simplify. x + (x + 3d) - (x + d) = x + 2d or z.
Given the data from the question, the statement x + w - y = z is true See explanation below
What is an arithmetic sequence?
This is a type of sequence which have common difference between each term. It is represent mathematically as:
Tₙ = a + (n – 1)d
Where
- Tₙ is the nth term
- a is the first term
- n is the number of terms
- d is the common difference
Considering the question given
- Sequence => x, y, z, w
- 1st term = x
- 2nd term = y = x + d
- 3rd term = z = x + 2d
- 4th term = w = x + 3d
- NOTE: Common difference is d
How to prove that x + w - y = z
x + w - y = z
x + (x + 3d) - (x + d) = x + 2d
Clear bracket
x + x + 3d - x - d = x + 2d
x + x - x + 3d - d = x + 2d
x + 2d = x + 2d = z
Learn more about arithmetic sequence:
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