1. The Nature of Mathematics
Jimmy B. Imping

2. Mathematics in the Modern World
What is Math?
Definition
Appreciation
Application
Sequences and Series
Illustrstive Example
Finding the Terms in a Sequence
Fibonacci Sequence (Golden Ratio)
Patterns
Counting
Logic

3. Mathematics It is not just about numbers.
Much of it is Problem Solving and Reasoning

4. As an Entrep student, . . .
What is the Relevance of Mathematics for an Entrep Student like you?

5. APPRECIATION OF MATHEMATICS:
Resto Tip
Netflix view
Calculating Bills
Computing test scores
Handling money
Exercise
Countdown
Cooking and Baking

6. APPLICATION OF MATHEMATICS:
Economics
Actuarial – Insurance and Financing
Logic
Management
Accounting

7. SEQUENCE AND SERIES
SEQUENCE is a function whose domain is the set of positive integers or set {1, 2, 3, , n}
SERIES represents the sum of the terms of a sequence.
SEQUENCE = List of numbers separated by commas.
SERIES = Sum of numbers separated by “+” or “-” sign.

8. SEQUENCE AND SERIES 1) 9 + 12 + 15 + 18 + 21 + . . . + 451)
2) 1, ½, 1/3, ¼, , 1/8
3) -15, -9, -3, 3, . . ., 15 4)
5) 1, 1/10, 1/100, 1/1000, 1/10000, , 1/

9. SEQUENCE AND SERIES
The sequence with nTH term is usually denoted by {An} and the associated series given by:
S = A1 + A2 + A An
e.g., 5 term (Associated Series)
S = A1 + A2 + A3 + A4 + A5
A1 = first term, A5 = last term

10. Illustrative Example 25 50 175 , . . . n
Marilyn helps her mother in selling brownies. From the money that her mother is giving her, she plans to save Php25.oo. For the next seven weeks, the amount of money she will have will form the following sequence:
25, 50, 75, 100, 125, 150, 175
, n
The numbers in the sequence are called ‘terms’. In the given sequence, the first term is ________, the second term is __________ and the last term is _________. 25 50
175

11. Finding the Terms of the Sequence
Example: An = 2n + 1, Asked to get the first 5 terms:
A1 = 2(1) + 1 = 3
A2 = 2(2) + 1 = 5
A3 = 2n + 1 = 
A4 = 2n + 1 = 
A5 = 2n + 1 = 

12. Math-alas!? Math-inik!?
Find the first 4 terms of the sequence whose nTH term is An = 2 + 2n

13. Math-alas!? Math-inik!?
List the first five terms of the sequence given by An = (-1)n n2

14. Math-alas!? Math-inik!? An = n2 - 1
Find the 7th term, 13th term and the 25th term of the sequence whose nTH term is
An = n2 - 1
n2 + 1

15. Pinaka Math-alas!? Pinaka Math-inik!?
Find the seventh term of the sequence 1, 2, 5, , ½ (1 + 3 n-1), . . .