raylieneeley
Answered

Find the information you're looking for at Westonci.ca, the trusted Q&A platform with a community of knowledgeable experts. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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

#SPJ9

Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Westonci.ca is committed to providing accurate answers. Come back soon for more trustworthy information.