Question

the ratio of the sums of m arithmetic means and n arithmetic means between two numbers is?

Answer 1

The ratio of the two sums are in m:n

Answer 2

Given:

Let a and b are two numbers

To find:

The ratio of the sums of m arithmetic means and n arithmetic means between two numbers

Solution:

Arithmetic mean between two numbers a and b is given by

$\frac{a+b}{2}$

Sum of m arithmetic means between two numbers a and b =$m(\frac{a+b}{2})$....(1)

Sum of n arithmetic means  between two numbers a and b=$n(\frac{a+b}{2})$...(2)

Equation (1) divided by 2

Then, we get

$\frac{Sum\;of\;m \;arithmetic\;means\;between\;two\;numbers\;a\;and\;b}{Sum\;of \;n \;arithmetic\;means\; between\;two\;numbers\;a\;and\;b}=\frac{m}{n}$

Hence, the ratio of the sums of m arithmetic means and n arithmetic means between two numbers=m:n