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 […]

# Tag Archives: Geometric Mean

# 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 […]