When three numbers and are in A.P., then is average of and .
In general if are in A.P, their Arithmetic Mean A.M is defined as
The terms are called the Arithmetic Means between and .
Some Facts about an A.P
(i) If a fixed number is added to (subtracted from) each term of a given AP, then the resulting sequence is also an AP and it has the same common difference as that of the given AP.
(ii) If each term of an AP is multiplied by a fixed constant (or divided by a non-zero fixed constant), then the resulting sequence is also an AP.
(iii) If and are two Arithmetic Progressions, then is also an AP.
(iv) If we have to take three terms in AP whose sum is known, it is convenient to take them as . In general, if we take terms in AP, we take them as .
(v) The numbers are said to be Arithmetic Means between and , if is an AP.
Here is the first term and is the term of the AP.
If is the common difference of this AP, then