raylieneeley
Answered

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show that if x,y,z and w are the first four terms of an arithmetic sequence, then x+w-y=z

Sagot :

mLawson8922

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.

Eduard22sly

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:

https://brainly.com/question/16130064

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