Question

What is the A.M of three quantities $a + 2$ , $a$, $a - 2$

Answer 1

For the Arithmetic mean of any given numbers is the average of the numbers it is calculated by adding them together and dividing by the number of terms in the set.
Mean that the A.M $= \dfrac{{{\text{Sum of all the terms }}}}{{{\text{Total number of term }}}}$

Complete step by step solution:
In this question we have to find out the Arithmetic mean of the numbers $a + 2$ , $a$, $a - 2$
Basically it is the average of the number given number , as calculated by adding them together and dividing by the number of terms in the set.
mean that the A.M $= \dfrac{{{\text{Sum of all the terms }}}}{{{\text{Total number of term }}}}$
Hence in the given question the terms are $a + 2$ , $a$, $a - 2$ , total number of term is equal to $3$
So from the formula of Arithmetic mean that is ,
Arithmetic mean $= \dfrac{{{\text{Sum of all the terms }}}}{{{\text{Total number of term }}}}$
Arithmetic mean $= \dfrac{{a + 2 + a + a - 2}}{3}$
Hence $2$ will cancel out in denominator ,
Arithmetic mean $= \dfrac{{a + a + a}}{3}$
$= \dfrac{{3a}}{3}$
Hence $3$ will common in both numerator and denominator hence it will cancel out ,
Arithmetic mean =$a$

Hence the Arithmetic mean of the number $a + 2$ , $a$, $a - 2$ is $a$ .

Note:
Geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values .
GM of given numbers ${a_1},{a_2},{a_3}....................{a_n}$ is GM = ${\left( {{a_1},{a_2},{a_3}....................{a_n}} \right)^{\dfrac{1}{n}}}$
The harmonic mean is a type of numerical average that is calculated by dividing the number of observations by the reciprocal of each number in the series
HM of given numbers ${a_1},{a_2},{a_3}....................{a_n}$ is HM = $\dfrac{n}{{\dfrac{1}{{{a_1}}} + \dfrac{1}{{{a_2}}} + \dfrac{1}{{{a_3}}}..........\dfrac{1}{{{a_n}}}}}$