Find the A.M. between:

(i) 7 and 13 (ii) 12 and - 8 (iii) (x - y) and (x + y)

(i) Let A be the Arithmetic mean

Then 7, A, 13 are in AP

A-7 = 13-A

2A = 13 + 7

A = 10

(ii) Let A be the Arithmetic mean

Then 12, A, - 8 are in AP

A - 12 = - 8 - A

2A = 12 + 8

A = 2

(iii) Let A be the Arithmetic mean

Then x - y, A, x + y are in AP

A - (x - y) = (x + y) – A

2A = x + y + x - y

A = x