Question

Given two numbers $a$ and $b$, let $A$ denotes the single A.M. and $S$ denotes the sum of $n$ A.M.s between $a$ and $b$ then $\frac{S}{A}$ depends on

• A. $n,a,b$
• B. $n,b$
• C. $n,a$
• D. $n$

Answer 1

Answer: (D)

$n$

We know sum of $n$ A.Ms between $a$ and $b$ is, $S=\frac{n}{2}(a+b)$
and $1$ A.M between $a$ and $b$ is, $A=\frac{a+b}{2}$
Therefore, $\frac{S}{A}=n$
Clearly, $\frac{S}{A}$ depends on $n$.
Hence, option 'D' is correct.