Arithmetoc sequence and series example problems and presenation

1. Arithmetic Sequences and
Series
September 06, 2021

2. Arithmetic Sequence
A sequence, in which a constant, d, is
added to the previous term to get the
next term is called arithmetic
sequence. The constant is called the
common difference. The common
difference can be positive (the terms of
the sequence are increasing in value)
or negative (the terms of the sequence
are decreasing in value).

3. Identifying an Arithmetic
Sequence
2, 4, 8, 14, 22,
…
4, 10, 16, 22,
28, …

4. Arithmetic Sequence Formula

5. Example 1
• Find the 16th term of the sequence 1, 5, 9,
13, …

6. Example 2
• Find the nth term of the sequence 3, 7, 11, 15,
…

7. Example 3
• In the sequence 50, 45, 40, 35, …, which
term is 5?

8. Seatwork
• Find the 20th term of the sequence 25, 23, 21, 19, 17, …
• Find the nth term of this sequence 2, 8, 14, 20, …
• In the sequence 7, 10, 13, 16, …, which term is 43?

9. More Examples!!
In the sequence -1, 3, 7, 11, …, which term is 27?

10. More Examples!!
Find the NEXT THREE TERMS of the following arithmetic
sequence:
1, 2 ½, 4, 5 ½ , ….

11. Arithmetic Series
The sum of the terms of a sequence is
called Arithmetic Series
An infinite series is the sum of the
series of an infinite sequence.
A partial sum, also called finite series,
denoted by 𝑆𝑛, is the sum of the first n
terms in a finite sequence.

12. Summation Notation
• Shorthand way of expressing a sum
• Denoted by the Greek letter Σ

13. Summation Notation Properties

17. Homework
Given the sequence continues, give the nth
term of the sequence and find the 12th term
using the obtained nth term
Express each sum using summation notation

18. Homework
Find each indicated sum