Let `n in N ,n > 25.` Let `A ,G ,H` deonote te arithmetic mean, geometric man, and harmonic mean of 25 and `ndot` The least value of `n` for which `A ,G ,H in {25 , 26 , n}` is a. 49 b. 81 c.169 d. 225

Options

A. 49
B. 81
C. 169
D. 225

Explanation

To solve the problem, we need to find the least value of \( n \) such that the arithmetic mean (A), geometric mean (G), and harmonic mean (H) of the numbers 25 and \( n \) belong to the set \( \{25, 26, n\} \).

### Step-by-step Solution:

1. **Define the Means**:
- The **Arithmetic Mean (A)** of two numbers \( a \) and \( b \) is given by:
\[
A = \frac{a + b}{2}
...