Q.Insert a Geometric Mean between 4 and 16, and verify that the resulting three numbers form a GP.

The Geometric Mean of two positive numbers $a$ and $b$ is $G=\sqrt{ab}$, the value that makes $a, G, b$ a three-term GP. …

Given: two numbers, 4 and 16; insert their Geometric Mean.

Step 1 — Apply the GM formula: $G = \sqrt{ab} = \sqrt{4 \times 16} = \sqrt{64}$.

Step 2 — Simplify the square root: $\sqrt{64} = 8$.

Step 3 — State the resulting GP: $4, 8, 16$. …

Using the Arithmetic Mean formula $(a+b)/2$ instead of the Geometric Mean formula $\sqrt{ab}$ — for 4 and 16 these give different values (AM $ …