Arithmetic Mean

Step 1: Understand the concept of Arithmetic Mean.
The Arithmetic Mean (A.M.) of two numbers

a

and

b

is given by:

A.M.%3Cbr%3E%3D%20%5Cfrac%7Ba%20%2B%20b%7D%7B2%7D

We are asked to find the value of

n

for which:

%5Cfrac%7Ba%5E%7Bn%2B1%7D%20%2B%20b%5E%7Bn%2B1%7D%7D%7Ba%5En%20%2B%20b%5En%7D

is the A.M.
between

a

and

b

.
Step 2: Set up the equation.
For the given expression to be the A.M.
between

a

and

b

, it should be equal to:

%5Cfrac%7Ba%20%2B%20b%7D%7B2%7D

Step 3: Analyze the expression.
Let’s simplify the given expression for different values of

n

.
The value of

n

that satisfies the equation is found to be 1, as this makes the expression equal to

%5Cfrac%7Ba%20%2B%20b%7D%7B2%7D

.
Step 4: Conclusion.
Therefore, the value of

n

for which the expression is the A.M.
between

a

and

b

is 1.

Chapter Questions
1 MCQs