This document differentiates between finite and infinite geometric sequences. It defines a geometric sequence as a sequence where each term after the first is obtained by multiplying the preceding term by a constant ratio. A finite geometric sequence has a first and last term, while an infinite geometric sequence goes on forever, indicated by three dots. Examples are provided of sequences and whether they are finite or infinite. The key characteristics for identification are whether the sequence has a limit or goes on forever.

1. Differentiating Finite Geometric Sequence
from an Infinite Geometric Sequence.

2. LET’S GROUFIE
With your own set of criteria, group the following:
•Line
•Line segment
•1, 2, 3, 4, 5, … 100
•1, 2, 3, 5, 7, 11, 13, 17, …
•Natural numbers
•Even numbers less than 50

3. In the previous discussions, geometric sequence
is a sequence where each term after the first is
obtained by multiplying the preceding term by a
nonzero constant called the common ratio.
There are two types of geometric
sequence namely: finite geometric sequence
and infinite geometric sequence.
Into what aspect they differ, that’s for us
to find out.

4. FINDING OUT
•Group A are items which suggest limit thus it is
considered finite.
•Group B are items whose last value cannot be
determined. It has no limit; therefore, they are
infinite.

5. State whether each of the following
geometric sequences is finite or infinite.
•1) 4, 12, 36, 108,….
•2) 2, 6, 18, 54, 162
•3) 7, 14, 28, 56, 112 …
•4) -3, 3, -3, 3
•5)
3
4
,
3
4
,
3
4
,
3
4
, …

6. •1. How do you find doing the activity?
•2. Which of the items are finite geometric
sequence and which are infinite geometric
sequences?
•3. What are the important characteristics that you
should remember in identifying finite or infinite
geometric sequence?

7. •Finite sequence is a function whose domain
is the finite set { 1, 2, 3, …, n }. They have a
first and a last term.
•Infinite sequence is a function whose
domain is infinite set { 1, 2, 3, …}. A
sequence that goes on forever, indicated by
three dots following the last listed number.

8. ASSIGNMENT
•List down 5 examples of
finite geometric sequence
and 5 example of infinite
geometric sequence.

9. •"The only limit to our
realization of
tomorrow will be our
doubts of today.“
— Franklin D. Roosevelt

10. Franklin D. Roosevelt
(January 30, 1882 – April 12,
1945), commonly known by his
initials FDR, was an American
politician who served as the 32nd
president of the United States
from 1933 until his death in 1945