# Arithmetic Sequences

Algebraic Definition An $\textit{Arithmetic Sequence}$ is a sequence in which each term differs from the previous one by the same fixed number, which is often called $\textit{common difference}$. It can also be referred to as an $\textit{arithmetic progression}$. A sequence in mathematics is an ordered set of numbers.An $\textit{arithmetic sequence}$ is one in which: the […]

# 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 […]