PRELIM 01 - Sequences and Series, Nature of Math

Question 1

Is a succession of numbers (called terms) that follow a given rule

Answer 1

Sequence

Question 2

A recurrence relation together with the first term of a sequence

Answer 2

Inductive definition

Question 3

In __________, the difference between any two consecutive terms is always the same

Answer 3

Arithmetic sequence

Question 4

Other name for arithmetic sequence

Answer 4

Arithmetic progression

Question 5

The sum of all the terms of a sequence

Answer 5

Series

Question 6

A famous mathematician that was asked by his teacher to add together every whole number from one to a hundred

Answer 6

Karl Friedrich Gauss

Question 7

Greek symbol that means ‘the sum of’

Answer 7

Σ (sigma)

Question 8

The sum of the terms of an infinite geometric sequence

Answer 8

Geometric series

Question 9

Is a sequence of quantities whose reciprocals form an arithmetic progression

Answer 9

Harmonic progression

Question 10

The ancient Greeks considered the __________ to be the most aesthetically pleasing of all rectangular shapes

Answer 10

Golden rectangle

Question 11

The golden rectangle was used many times in the design of the famous Greek temple, the __________

Answer 11

Parthenon

Question 12

Mathematician who realized the advantages of the Hindu-Arabic system

Answer 12

Fibonacci

Question 13

Place where Fibonacci was born

Answer 13

Pisa, Italy

Question 14

Year when Fibonacci was born

Answer 14

1175 AD

Question 15

Full name of Fibonacci

Answer 15

Leonardo of Pisa/Leonardo Bigollo

Question 16

Were introduced in “The Book of Calculating”

Answer 16

Fibonacci numbers

Question 17

Arises from the Fibonacci numbers

Answer 17

Golden Ratio

Question 18

Golden ratio is represented by the Greek letter __________

Answer 18

Phi (Φ)

Question 19

Ratio of Phi

Answer 19

1:1.618 or 0.618:1

Question 20

He showed how to find the golden section of a line

Answer 20

Euclid

Question 21

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

Answer 21

Stradivari

Question 22

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

Answer 22

Baginsky

Question 23

Tool invented by Dr. Eddy Levin

Answer 23

Golden mean gauge