Sequence and Series

1. GOOD
MORNING
GRADE 10
MATHEMATICS 10
TEACHER JO’

2. Understanding
Patterns in
Sequences and
Series
This presentation explores the fundamental
concepts and applications of sequences and series
in mathematics for deeper understanding and
practical use.
Math Insights

3. TABLE OF
CONTENTS

4. Sequences
• an ordered lists of numbers
that follow a specific pattern.
• a function whose domain is
the set of positive integers.
• Term - number in sequence
INTRODUCTION TO
SEQUENCES

5. The {1, 3, 5, 7, 9 } form a sequence. The sum of
the terms of the sequence forms a series.
SEQUENCES VS SERIES

6. A finite series is a
sequence of
numbers that has
a specific end
point and can be
Finite Series
(Partial Sum) An infinite series
continues
indefinitely and
does not have an
end point, leading to
unique
mathematical
Infinite Series
Convergence occurs
when a series
approaches a limit,
while divergence
indicates that it does
not settle to a specific
Convergence vs
Divergence
TYPES OF SERIES

7. SUMMATION NOTATION
A concise way of of writing a series.
Sigma (Σ) = a Greek letter which tells to sum or add up terms.
k = the index of the summation which tells you where to start the
and gives the lower limit of the summation.
n = tells you where to end and also called as the upper limit of the
summation
Where in:

8. EXAMPLE # 1
Find its indicated sum

9. EXAMPLE # 2
Express the sum using summation notation

10. Quiz 1(20 pts)
Express the sum using
summation notation
Find each indicated sum