if x,y,z represents consecutive terms in an Arithmetic progression, prove that y is = (x+z)/2

Answer 1

State that the difference to be 'b'
y = x + b
b = y - x. ..(1)

z = y + b = x + 2b
b = (z - x)/2. ..(2)

Combining equations (1) and (2):
b = y - x = (z - x)/2
y = (z + x)/2