General Mathematics 1

Vocabulary flashcards covering mathematical patterns, sequences, series, sigma notation, compound interest, and types of annuities based on the provided lecture notes.

Fibonacci Sequence

A list of numbers where each number is the sum of the two numbers right before it, usually starting with 0 and 1, making the pattern: 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

Pattern

A repeated or predictable arrangement of numbers, shapes, objects, or events.

Sequence

An ordered list of numbers.

Term (of a sequence)

Each individual value in an ordered list of numbers.

Leonardo of Pisa (Fibonacci)

An Italian mathematician who introduced the Fibonacci sequence to Europe in his influential book, Liber Abaci (The Book of Calculation), published in 1202.

Liber Abaci (The Book of Calculation)

An influential book published in 1202 by Leonardo of Pisa in which he introduced the Fibonacci sequence to Europe.

Arithmetic Sequence

A sequence in which each term is found by adding or subtracting a constant number called the common difference ($d$).

Common Difference ($d$)

The constant number added or subtracted to find each term in an arithmetic sequence.

Arithmetic Series

The sum of the terms in an arithmetic sequence connected by plus signs.

Geometric Sequence

A sequence in which each term is found by multiplying or dividing by a constant non-zero number called the common ratio ($r$).

Common Ratio ($r$)

The constant non-zero number used to multiply or divide to find each term in a geometric sequence.

Finite Sequence

A sequence that has a limited or fixed number of terms, with a first term and a last term.

Infinite Sequence

A sequence that continues indefinitely with no last term, using an ellipsis (…) to indicate that the pattern goes on forever.

Geometric Series

An expression formed by adding the terms of a geometric sequence, representing the sum of all or some terms in a geometric sequence.

Sigma Notation

A notation style that uses the Greek letter $\sum$ (sigma) to represent sum.

Sigma Symbol ($\sum$)

The Greek letter in sigma notation that means add or sum.

Index ($k$)

The counting variable or expression (rule) to be added in sigma notation.

Compound Interest

Interest calculated on the initial principal and on the accumulated interest of previous periods.

Principal ($P$)

The original amount of money invested or borrowed.

Interest ($I$)

The amount earned or paid for using money.

Future Value / Maturity Value ($F$ or $A$)

The total value of money after a certain period, including interest.

Time ($t$)

The length of investment or loan in years.

Nominal Interest Rate ($r$)

The stated annual interest rate, not yet adjusted for compounding.

Compounding Frequency ($n$)

How many times interest is applied per year.

Annuity

A financial contract with an insurance company or bank where you make regular payments or a lump sum in exchange for a steady stream of future income, usually used during retirement.

Simple Annuity

An annuity in which the payment interval is the same as the compounding period.

General Annuity

An annuity in which the payment interval does not match the interest compounding period.

Deferred Annuity

An annuity whose term does not begin immediately but starts after a specified delay or deferral period ($d$).