At the endof the lesson, you are
expected to:
1. generate pattern from a given
succession of objects, numbers,
letters, or symbols;
2. find the nth term of a sequence;
and
3. write the rule for the nth term of a
sequence.
What is asequence?
A sequence is a set of objects which is
listed in a specific order, one after another.
Each member or element in the sequence is
called term.
The terms in a sequence can be written as
𝒂𝟏, 𝒂𝟐, 𝒂𝟑, 𝒂𝟒, ... ,𝒂𝒏, ... which means 𝑎1 is
the first term, 𝑎2 is the second term, 𝑎3 is
the third term, …, 𝑎𝑛 is the nth term, and so
15.
1st
Term
nth term (aterm's position
in the sequence)
a1
Position or order
of the terms
n
an
16.
Sequences can beclassified as either
finite sequence or infinite sequence.
Finite Infinite
• has limited
number of terms
• it has an end or
last term
• has countless
number of terms
• it continues
without stopping
17.
1. The firstfive natural number.
2. The set of even whole numbers.
3. The multiples of 4 up to the 40.
4. The sequence of the multiples of three
FINITE
INFINITE
INFINITE
FINITE
3, 6, 9, 12, 15, 18,…
2, 4, 6, 8, 10, 12, 14, 16, …
4, 8, 12, 16, 20, 24, 28, 32, 36, 40
1, 2, 3, 4, 5
18.
Finding terms ofa sequence
A term in a sequence can be
identified using a general
term.
A general term or the nth
term is usually expressed as
an equation.
19.
How to finda term of a sequence
using a general term?
Consider the following steps:
1. Substitute the value of n.
2. Perform the operations.
3. Simplify.
20.
Example:
Find the firstfive terms of the
sequence an = 5n – 2.
Remember that n denotes
the position or order of the
terms.
21.
Solution: Find thefirst five terms of the
sequence an = 5n – 2.
an = 5n – 2
For the first term, n = 1
an = 5n – 2
a1 = 5(1) – 2
a1 = 5 – 2
a1 = 3
22.
Solution: Find thefirst five terms of the
sequence an = 5n – 2.
For the second term,
n = 2
an = 5n – 2
a2 = 5(2) – 2
a2 = 10 – 2
a2 = 8
For the third term,
n = 3
an = 5n – 2
a3 = 5(3) – 2
a3 = 15 – 2
a3 = 13
23.
Solution: Find thefirst five terms of the
sequence an = 5n – 2.
For the fourth term,
n = 4
an = 5n – 2
a4 = 5(4) – 2
a4 = 20 – 2
a4 = 18
For the fifth term,
n = 5
an = 5n – 2
a5 = 5(5) – 2
a5 = 25 – 2
a5 = 23
24.
Answer:
Find the firstfive terms of the
sequence an = 5n – 2.
The first five terms of the
sequence an = 5n – 2 are
3, 8, 13, 18, and 23.
