14.1.3. Question Number 8

Try these first

1. 1.

   Calculate the arithmetic mean and geometric mean of 4 and 9.

   Hint

   Remember the formulas for AM and GM.

2. 2.

   What is the geometric mean of 25 and 100?

   Hint

   Use the formula GM = √(x1 * x2).

3. 3.

   What is the formula for the Arithmetic Mean?

   • (x1 + x2 + ... + xn) / n
   • (x1 * x2 * ... * xn)^(1/n)
   • None

   Hint

   What does an average represent?

4. 4.

   Is it true that the AM is always greater than or equal to the GM?

   • True
   • False

   Hint

   Reflect on the properties of squares.

5. 5.

   Propose a set of four different positive real numbers and compute both their AM and GM. Confirm they meet AM ≥ GM.

   Hint

   Start by calculating their sum for AM and product for GM.

6. 6.

   In the context of AM ≥ GM, illustrate the significance of the proof by applying it in a real-world scenario, such as finance or population growth.

   Hint

   Consider investments yielding different interest rates.