1. The document instructs readers to fold a square piece of paper into quarters and record the resulting areas in a table after each fold. 2. It starts with a square of area 64 square units and folds the corners into the center, halving the side length and quartering the area each time. 3. The reader is to repeat this folding process three times and record the resulting areas in a provided table.

2. Do the activity with a partner. One of you will perform the paper
folding while the other will do the recording in the table.
1. Start with a big square from a piece of paper. Assume the area
of the square is 64 square units.
2. Fold the four corners to the center of the square and find the
area of the resulting square.
3. Repeat the process three times and record the results in the
table below.
Square 1 2 3
Area

3. 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.

4. Problem:
What are the first 5 terms of a
geometric sequence whose first term
is 2 and whose common ratio is 3?
Given the first term a1 and the
common ratio r of a geometric
sequence, the nth term of a
geometric sequence is _

5. Example:
What is the 10th term of the geometric sequence 8, 4,
2, 1, …?
Solution:
The 10th
term is
1
64

6. Geometric Mean
A geometric mean is a number
inserted between any two given
numbers so that the terms form
geometric sequence.

7. Example:
Insert two geometric
means between 3
and 192.

8. Solution:
The geometric
means between 3
and 192 are 12
and 48.

9. Sum of Geometric Sequence
The formula of the first n terms of a geometric
sequence is

10. Examples:
A. Find the sum of the seven terms of geometric sequence 3, 6,
12, 24.
Solution:

11. B. Find the sum of the geometric sequence
40, -20, 10, -5, 5/2, -5/4.
Solution:

12. Quiz
1. Write the first five terms of a geometric
sequence whose first term is 2 and whose
common ratio is 3.
2. Insert three geometric means between -3
and 96.
3. Find the sum of the first 5 terms of the
geometric sequence whose first term is 128
and its common ratio is one- half.