This document defines and provides examples of arithmetic sequences and series. It explains that an arithmetic sequence is a sequence where the difference between consecutive terms is constant. Examples of arithmetic sequences are provided. It also defines an arithmetic series as the sum of terms in an arithmetic sequence. A formula for calculating the general term and the sum of the first n terms of an arithmetic sequence is given. Examples of problems involving finding specific terms and sums are presented. References on the topic are listed at the end.

1. SEQUENCES AND
SERIES(ARITHMETIC)
BY MALULEKE PJ

2. SUM MATHEMATICIAN
•CARL FRIEDRICH GAUSS

3. • NATURE---DID YOU KNOW: UNDERSTANDING A SEQUENCE,
ILLUSTRATED BELOW IS A FIBONACCI SEQUENCE ONE OF THE
ANCIENT PATTERNS TO EVER BEING DISCOVERED BY MANKIND(JACOBS,2011)

4. ARITHMETIC SEQUENCE
•RIMANDO:IT IS A SEQUENCE IN
WHICH
THE
DIFFERENCE
BETWEEN
CONSECUTIVE
TERMS IS CONSTANT AND HAS
a THE FORM: 2d , , a n 1 d
, a d, a
1
1
• NOTE:
SEQUENCE
1
1
AN
ARITHMETIC

5. ARITHMETIC SEQUENCE
•EXAMPLES:
•
1, 4, 7, 10, 13, …
•
6, 11, 16, 21, 26, …
•
14, 25, 36, 47, 58, …
•
4, 2, 0, -2, -4, …
•
-1, -7, -13, -19, -25, …

6. ARITHMETIC SEQUENCE
•GENERAL TERM:
an
a1
n 1d

7. Example/s:
Find the 50th term of the
arithmetic sequence 2, 6, 10,
14, …

8. ARITHMETIC SERIES
S n a1 a
•A SERIES IS AN INDICATED SUM OF
TERMS OF A SEQUENCE. IF THE
TERMS FORM AN ARITHMETIC
SEQUENCE WITH FIRST TERM A1
AND COMMON DIFFERENCE D, THE
INDICATED SUM OF TERMS IS
CALLED AN ARITHMETIC SERIES.
THE SUM OF THE FIRST N TERMS,
REPRESENTED
AS
SN,
2
3
n 1
n
IS(GAUTANI,2011)
a
 a
a

9. ARITHMETIC SERIES
•LET SN = A1 + A2 + … + AN
BE
AN
ARITHMETIC
SERIES WITH CONSTANT
n 2a1 n 1 d
DIFFERENCE D, THEN:
Sn
2

10. ARITHMETIC SERIES
•LET SN = A1 + A2 + … + AN
BE
AN
ARITHMETIC
SERIES THEN a
na
Sn
1
n
2

11. Example/s:
Find the sum of the first 100
positive even numbers.

12. Reference:
Rimando, K. (2011), Sequences and
Series
Jacobs, J. (2011), Patterns and
Sequences
Gautani, V. (2011), Sequences and
series and binomial Theorem