powerpoint presentation

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.