When three quantities are in A.P., the middle one is said to be the arithmetic mean of the other two.
Thus, if a, b, c are three successive quantities in A.P., then "b" is called the arithmetic mean of a and c.
It is given by b =
Hence, arithmetic mean of two numbers is half of their sum i.e, their average.
(It may be noted that, while the AM used in A.P. is average of just two numbers, the term mean used in statistics is the average of entire set of data).
Properties of Arithmetic Progression:
1. If a, b, c are in A.P., then 2b = a + c
2. If a, b, c are in A.P. and k ≠ 0, then the following are also in A.P.
(i) a + k, b + k, c + k i.e, when k is added to each term
(ii) a – k, b – k, c – k i.e, when k is subtracted from each term
(iii) ak, bk, ck i.e, when each term is multiplied by k
(iv) a/k, b/k, c/k i.e, when each term is divided by k