Sequences, Series, and Measurement Systems Vocabulary

Vocabulary practice flashcards generated from lecture notes covering Sequences, Series, Scalar and Vector Quantities, Metric Systems, and Conversion Factors.

Sequence

A list of numbers or objects arranged in a specific order.

Pattern

A repeated arrangement of numbers or objects.

Pattern Rule

A rule that explains how one term becomes the next term in a sequence.

Fibonacci Sequence

A sequence formed by adding the two previous terms to get the next term.

Term

Any number or object in a sequence.

Position (Index)

An indicator that tells where a term is located in a sequence.

Notation

The system of using symbols to represent a term in a given sequence, such as $a_1$ for the first term.

Arithmetic Sequence

A sequence formed by adding a fixed number (Common Difference) to each and every term.

Geometric Sequence

A sequence formed by multiplying a fixed non-zero number (Common Ratio) to each and every term.

Finite Sequence

A sequence that has a specific number of terms.

Infinite Sequence

A sequence that has no end, follows the same rule endlessly, and ends with ellipses ($\dots$).

Common Difference ($d$)

The fixed number added to each term in an arithmetic sequence, where $d > 0$ indicates an increasing sequence and $d < 0$ indicates a decreasing sequence.

Numerical Representation

A method that uses numbers to represent a sequence.

Visual Representation

A method that utilizes graphical tools and uses images to represent sequences.

Arithmetic Sequence General Formula

The general formula $a_n = a_1 + (n-1)d$, where $a_n$ is the $n\text{th}$ term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.

Series

The operation or result of adding all terms in any sequence.

Arithmetic Series

The sum of the terms of an arithmetic sequence, calculated using $S_n = \frac{n}{2}(a_1 + a_n)$ or $S_n = \frac{n}{2}[2a_1 + (n-1)d]$.

Geometric Series

The sum of the numbers or terms in a geometric sequence.

Common Ratio

The constant multiplier used to calculate each subsequent term in a geometric sequence.

Quantity

A concept that explains how much or the amount of an object is.

Scalar Quantities

Quantities that can be expressed in terms of magnitude only and are completely specified by a number and unit.

Vector Quantities

Quantities that can be expressed in terms of magnitude and direction (N, E, W, S).

Metric System

A system of measurement in which the basic units are the meter, kilogram, and second, also known as the MKS System of Measurement.

Système Internationale d'Unités

The French name from which the International System of Units (Metric System) is derived.

Conversion Factors

Ratios that express the relationship between two different units of measurement for the same quantity.