Question

Prove that for a set of number in arithmetic sequence,the mean and median are equal

Answer 1

Answer:

The following theorem can be proved by using the facts about the terms of an AP and there formula

Let an arithmetic progression of n terms with common difference d

The AP would be like :

a- nd, a-(n-1)d, a-(n-2)d,............ a-d, a , a+d ,................ a+(n-2)d, a+(n-1)d, a+nd

The total number of terms would be 2n+1

Here, we can apprehend that any arithmetic progression can be written in this form.

The mean of this data would be

[a- nd +a-(n-1)d +a-(n-2)d+............ a-d+ a + a+d +................+ a+(n-2)d+ a+(n-1)d+ a+nd] / 2n+1

a*(2n+1)/(2n+1)  = a

The sequence would already be sorted in increasing order, hence median would be middle most term i.e. a

Step-by-step explanation: