# Geometric Sequence and Geometric Mean

Geometric Sequence Definition Geometric Sequences are sequences where each term is obtained by multiplying the preceding term by a certain constant factor, which is often called $\textit{common ratio}$. A geometric sequence is also referred to as a $\textit{geometric progression}$. David expects $10$% increase per month to deposit to his account. A $10$% increase per month […]

# Inequalities using Arithmetic Mean Geometric Mean

Arithmetic Mean of $a$ and $b$ is always greater than or equal to the Geometric Mean of $a$ and $b$, for all positive real numbers with with equality if and only if $a = b$. This is also called AM-GM (Arithmetic Mean Geometric Mean) inequality. $\require{color}$  \begin{aligned} \frac{a + b}{2} \ge \sqrt{ab} \text{ or […]