The document provides examples of finding the general term of different sequences. For each sequence, it identifies the pattern between the terms and determines the formula for the nth term. The general terms provided are: 1) f(n) = 2n for the sequence 2, 4, 6, 8,... 2) f(n) = 2n - 1 for the sequence 1, 3, 5, 7,... 3) f(n) = 2n for the sequence 2, 4, 8, 16,... 4) f(n) = n^2 for the sequence 1, 4, 9, 16,... It also provides guidelines for finding the general term such as looking for a common difference,

1. Finding General Term of a
Sequence

2. Example 1. Find the general term of the
sequence 2, 4, 6, 8, …
Solution Observe the following.
2 = 2(1) – means 1st term
4 = 2(2) - 2nd term
6 = 2(3) - 3rd term
8 = 2(4) - 4th term
⋮ ⋮
The pattern is 2n where n = 1, 2, 3, 4, … or n is the position of each term in a sequence.
So, the general term of the sequence is f(n) = 2n.

3. Example 2. Find the general term of the
sequence 1, 3, 5, 7, …
Solution Observe the following.
1 = 2(1) – 1
3 = 2(2) – 1
5 = 2(3) – 1
7 = 2(4) – 1
⋮ ⋮
The pattern is 2n – 1 where n = {1, 2, 3, 4, …}.
So, the general term of the sequence is f(n) = 2n – 1.

4. Example 3. Find the general term of the
sequence 2, 4, 8, 16, …
Solution We can express in this manner:
2 = 21
4 = 22
8 = 23
16 = 24
⋮ ⋮
The pattern is is 2n where n = {1, 2, 3, 4, …}.
So, the general term of the sequence is f(n) = 2n.

5. Example 4. Find the general term of the
sequence 1, 4, 9, 16, …
Solution We can be express each term in the
following manner:
1 = (1)2
4 = (2)2
9 = (3)2
16 = (4)2
⋮ ⋮
The pattern is n2 where n = {1, 2, 3, 4, …}.
So, the general term of the sequence is f(n) = n2 .

6. Theres no definite way or rule in finding the nth term of
a given sequences. The following are helpful guide.
• 1. Find out if there is a common difference between two terms of
the given sequence of numbers.
• 2. Find out if there is a common factor among the terms of the
given sequences of numbers.
• 3. Find out if the given sequence is expressible in exponential form
with a common base.