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Mathematics in the Modern World
1RDT-A) | BATCH 2025
COLLEGE OF RADIOLOGY – FEU-NICANOR REYES MEDICAL FOUNDATION
TRANSCRIBED BY: Arota, Bicada, Dumanon, Enriquez,
Ladanga, Maraggun
LECTURER/S: Mr
...

REFERENCES: PPT, Handouts, Internet, textbook

PPT
Black

Professor
Mr
...


Textbook
Mathematics
in Modern
World

NATURE OF MATHEMATICS

1
2
3

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WHAT IS MATHEMATICS?
Mathematics means many things to many
people
...

Mathematics is unique in that it can be both
tangible yet completely abstract
(intangible) at the same time
...
Though there
are many different tongues on the planet,
there’s one common form of mathematics
...
It has been shown that
some animals, e
...
, crows, demonstrate the
rudiments of counting
...

 Oscar--winning film A beautiful Mind
 Dan Brown’s Bestseller The Da Vinci Code
 Academy Award-winning film Good Will
Hunting
 The Bigbang Theory
 The Man who knew Infinity
 Note: {} = the set of / = element of

Nature of Mathematics
LOGIC PATTERNS
Pattern – is an arrangement which helps observers
anticipate what they might see or what happens next
...

 To construct or solve a pattern, find the rule
for the pattern, understand the nature of the
sequence , analyze the difference between the two
successive terms
...

Finite Sequence Function
Example:
っ
っ
Corresponding Sequence:
Infinite Sequence Function:
っ
っ
Example:
Corresponding Sequence: っ

BS RADIOLOGIC TECHNOLOGY| BATCH 2025

っ

っ

っ

っ

ARITHMETIC SEQUENCE
Arithmetic  Is a sequence for which any
Sequence element, except the first, can be
obtained by adding a constant to the
preceding element
...

Formula: The number of elements is
denoted by n, the first element is
denoted by a1, and the last element
is denoted by an
...

E
X
A
M
P
L
E
S:

(1)
Common Difference: 2
Solution:
っっ
Answer:

(2)What should be the next number?
っ
Common Difference: -2
−
Solution:
Answer:
(3) What should be the next number?
っ っっ っ
Common Difference: 5
Solution:
っ
っ
Answer:

Formula:

E
X
A
M
P
L
E
S:

Number Patterns
 the nth element of an Arithmetic
Sequence is given by:
っ
−っ

...

Given: っ
Find:
Solution:
−っ

( To get the constant addend: − っ )
 9-5=4 d=4

Answer:
っ っ
(2) Find the first element of an arithmetic

2
BS RADIOLOGIC TECHNOLOGY | BATCH 2025

sequence whose common difference is-5,
and whose eighteenth element is -21
...
)
 Therefore, っ
っ − っ −っ −
 っ − っ− っ −
 っ − っ−
Answer: っ

GEOMETRIC SEQUENCE
Geometric  Is a sequence such that any
Sequence element after the first can be
obtained by multiplying the
preceding element by a constant
...

Constant  Then the Constant Multiplier
Multiplier (common ratio) is 2 – “All the
(d)
number are multiplied by 2”
Formula: 
っ

...


(1) Find the Tenth element of the geometric
sequence for which the first element is

A
M
P
L
E
S:

52 then the second element is -5
...

an+1=an+d
Step 2: If the sequence from step 1 has no
common difference, test for a common ratio, r,
and is a geometric sequence
...


Note: Always find the constant multiplier
and remember the formula when finding the
nth term
...

An example would be 1, 2, 3, 2, 1, 2, 3, 2, 1…
The terms in the sequence all differ by 1, but
sometimes 1 is being added and other times it is
being subtracted, so the sequence is not
arithmetic
...
14
31 ÷ 15 = 2
...
03
The sequence is not arithmetic
...
75
The sequence is not arithmetic nor geometric
...
The
Fibonacci Sequence always starts with either 0 or
1
...


FORMULAS
(a) Fn= Fn-1 + Fn-2 (where Fn is the unknown
number we have to solve for) and 2 or more terms
are given already in the sequence
...

(b) Binet Formula for getting the nth Fibonacci
number:
っ

−

っ

EXAMPLES
Find the 7 Fibonacci number given that the 6th
term is 8 and the 5th term is 5
...
So, we have:
F7 = F7-1 + F7-2
F7 =F6 + F5
This number sentences means that for us to get
the 7th term of the Fibonacci Sequence, we should
add the 6th and 5th term
...
13 is the 7th Fibonacci
number
...
What is the eighteenth?
F18 = F18-1 + F18-2
= F17 + F16
= 1597 + 987
F18 = 2584
The 18th Fibonacci number is 2584
...

You will need a scientific calculator for solving
this problem
...


4
BS RADIOLOGIC TECHNOLOGY | BATCH 2025

Answer: F50 = 12, 586, 270, 000
NATURE PATTERNS
The Fibonacci Sequence occurs many times in
nature
...

 Daisy- can also have petals which match
the Fibonacci numbers (13, 21, 34, 55,
89, )

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