The document defines a sequence as a function whose domain consists of consecutive positive integers starting from 1. Each term is denoted by a(n) where n is the position in the sequence. Sequences can be finite, ending at a set number of terms, or infinite, continuing indefinitely. Examples show common sequences and their terms. The rest of the document provides examples of finding terms of sequences given their general nth term rules and prompts activities to practice finding early terms using stated rules.

1. SEQUENCE
AND SERIES

2. Sequence
- a function whose domain consists of consecutive
positive integers starting from 1. If a is a sequence, its
terms are the values
a(1) , a(2) , a(3), . . .
with a(1) as the first term, a(2) as the second term,
and so on.

3. Examples of Sequences
• 1, 4, 7,10, 13
• 0, 1, 2, 0, 1, 2, 0, 1, 2
• 0, 5, 10, 15, 20, 25, . . .

4. Infinite Sequence
- sequence whose domain is the set of all
positive integers.
Finite Sequence
- sequence whose domain is the first n
positive integers.

5. General Terms of Sequences
EXAMPLE NO. 1
The nth term of a sequence with 20
terms is denoted by an = 3n + 1.
Find its first four terms and its twentieth
term.

8. General Terms of Sequences
EXAMPLE NO. 2
The nth term of an infinite sequence
is denoted by
an = (-1)n •
5
𝑛
Find a1 , a2, a5 and a10

11. EXAMPLE NO. 3
The terms of a sequence are
described by the following rule:
a1 = 5
an = an – 1 -2 if n > 1
Find a2, a3 , a4, and a5

13. ACTIVITY NO. 1

14. 𝑎𝑛 = 3𝑛
𝑎𝑛 = 2 − 𝑛
𝑎𝑛 = 4𝑛 − 1 𝑎𝑛 = 3𝑛
− 1
𝑎𝑛 =
1
𝑛 + 1
Given the nth term an , find the first four
terms of each sequence.
ACTIVITY NO.
1

15. 𝑎𝑛 = 3𝑛
− 1
Given the nth term an , find the first four
terms of each sequence.
ACTIVITY NO.
1

16. 𝑎1 = 2 and 𝑎𝑛 = 𝑎𝑛−1 + 3 𝑓𝑜𝑟 𝑛 > 1
Find the first three terms of each sequence using
the given rule.
𝑎1 = 5 and 𝑎𝑛 = 2𝑎𝑛−1 − 1 𝑓𝑜𝑟 𝑛 > 1

17. 𝑎1 = 2 and 𝑎𝑛 = 𝑎𝑛−1 + 3 𝑓𝑜𝑟 𝑛 > 1