The numbers x, y, and z are the first three terms of an arithmetic sequence. How do you express z in terms of x and y?

1 Answer
Jun 24, 2018

Answer:

Assuming #r# is the constant difference between two consecutive terms, you express #z=y+r# in terms of #y# and #z=x+2r# in terms of #x#.

Explanation:

Each arithmetic sequence has a starting point #x_0# and a particular number #r#.

You get the next term by adding the constant number #n# to the previous term.

So, the first term is #x_0#, which is given.

The second term is #x_0+r#

The third term is again #(x_0+r)+r= x_0+2r#. Remember the rule: always add #r# to the previous term to get the next.

So, if the first term is #x#, you have

#y=x+r,\qquad z=y+r#

This is how you express #z# in terms of #y#. If you want to express #z# in terms of #x#, plug the expression for #y# in the expression for #z#:

#z=color(red)(y)+r = color(red)((x+r))+r=x+2r#

and so #z=x+2r# is how you express #z# in terms of #x#