sequence and series

Question 1

a succession of numbers, called terms, that follow a given rule.

For example: 9, 16, 25, 36, 49, …

can be finite or infinite

Answer 1

sequence

Question 2

A sequence can be defined by:

Answer 2

• formula for the nth term of the sequence
• recurrence relation together with the first term of the sequence

Question 3

The nth term, or the _______, of a sequence is often given using ______ (or suffix) notation as un.

Answer 3

general term

superscript or suffix

Question 4

sequence can also be defined by a _______

Answer 4

recurrence relation

Question 5

A recurrence relation together with the first term of a sequence is called an ___________

Answer 5

inductive definition

Question 6

In an arithmetic sequence (or arithmetic progression) the difference between any two consecutive terms is always the same. This is called the __________.

Answer 6

common difference

Question 7

The sum of all the terms of a sequence is called a ______.

Answer 7

series

Question 8

When the difference between each term in a series is constant, as in this example, the series is called an _______ or _________.

Answer 8

arithmetic series or arithmetic progression (AP for short)

Question 9

When working with series, the Greek symbol Σ (the capital letter sigma) is used to mean

Answer 9

“the sum of”

Question 10

A sequence is _______ if the ratios of consecutive terms are the same.

Answer 10

geometric

Question 11

The sum of the first n terms of a sequence is represented by ___________.

Answer 11

summation notation

Question 12

A _________ is a sequence of quantities whose reciprocals form an arithmetic progression.

Answer 12

harmonic progression

Question 13

• Born in Pisa, Italy in 1175 AD
• Met with many merchants and learned their systems of arithmetic
• Realized the advantages of the Hindu-Arabic system

Answer 13

Fibonacci
Leonardo Pisa

Question 14

• Were introduced in The Book of Calculating
• Series begins with 0 and 1
• Next number is found by adding the last two numbers together
• Number obtained is the next number in the series
• Pattern is repeated over and over

Answer 14

The Fibonacci Numbers

Question 15

• can be found in the shape of playing cards, windows, book covers, file cards, ancient buildings, and modern skyscrapers.
• Many artists have incorporated this into their works because of its aesthetic appeal.

Answer 15

golden rectangle

Question 16

• ancient Greeks considered this to be the most aesthetically pleasing of all rectangular shapes.
• it was used many times in the design of the famous Greek temple, the Parthenon.

Answer 16

golden rectangle

Question 17

~ Represented by the Greek letter Phi
~ Phi equals ± 1.6180339887 … and ± 0.6180339887 …
~ Ratio of Phi is 1 : 1.618 or 0.618 : 1
~ Mathematical definition is Phi2 = Phi + 1
~ Euclid showed how to find the golden section of a line

Answer 17

golden ratio

Question 18

is the positive root of a quadratic equation and is called the golden section/ratio

Answer 18

limit

Question 19

used the golden section to place the f-holes in his famous violins

Answer 19

stradivari

Question 20

used the golden section to construct the contour and arch of violins

Answer 20

baginsky

Question 21

Golden Mean Gauge is invented by

Answer 21

Dr. Eddy Levin DDS