Question

Find the Arithmetic mean of the following sequence a-2,a , a+2

Answer 1

Hint:- Arithmetic mean is the average of all numbers in a set. Here add the 3 numbers in the given sequence and divide it by 3 to find A.M.

Given, an arithmetic sequence a-2,a , a+2.
An arithmetic sequence is a set of numbers with a definite pattern. There is a constant difference in all pairs of consecutive or successive numbers. E.g. 2,3,4,5.
We have constant difference ‘2’ in the arithmetic sequence a-2,a,a+2. Each term is having a constant difference of 2 from the consecutive term.
Now, A.M. stands for arithmetic mean. It is the ratio of the sum of all numbers present in the arithmetic sequence to the number of numbers present in the arithmetic sequence. In simple words, it is the average of all the numbers present in the arithmetic sequence.
Sum of all the numbers in the arithmetic sequence = a-2 +a+a+2
                                                                                            =3a
Number of terms in the sequence = 3.
So, A.M. = ${\displaystyle \frac{3\text{a}}{3}}$= a.
Hence, the arithmetic mean or A.M. of the given sequence is a.

Note:- There are three types of defined sequence available. They are arithmetic , geometric and harmonic. In arithmetic sequences each consecutive term can be obtained by adding a constant difference to the last term.