This document discusses generating a formula for sequences. It provides an example of a sequence representing the number of parents over 10 generations. The sequence is 1, 2, 4, 8, etc, where each term doubles the previous term. It then lists the steps to derive the formula for a sequence as: 1) determine the pattern, 2) express each term as a sum involving the pattern, 3) follow the pattern to find later terms, and 4) describe the equation. It asks the reader to find the formula for several example sequences and lists sequences to derive the formula for.

1. SEQUENCES
GENERATING A FORMULA
Solomon Hippocrates S. Flores
E. Rodriguez Vocational High School

2. Every family starts off
with a dad marrying a
mom. From there, the
mom and dad will have
children. Those children
in turn, then have their
own kids. Those kids will
eventually have more
kids of their own. How
many parents will there
be after 10 generations?

3. The above situation will give us the
following list:
1, 2, 4, 8, …
The numbers are listed in such a
way that 1 represents the dad, 2 mom and
dad, 4 being their children which
eventually be parents of 8 kids until the
10th generation.

4. In the presented sequence, we
designate a1 = 1 for the dad, a2 = 2 for
the mom and dad, a3 = 4 for their
children which will eventually be
parents. a4 = 8 for their kids and a10
for the 10th generation.

5. Since a sequence is a succession of
numbers which follows a fixed pattern, we
can derive the equation by looking at the
pattern by trial and error.
a. Determine the pattern.
b. Express each term as a sum of a
number and the pattern observed.
c. Follow the pattern to find an .
d. Describe the equation of the
sequence.

6. Find the general formula described by
the following sequence:
1) 5, 6, 7, 8, …

8. 3) 3, 5, 7, 9, …

10. 5) 4, 7, 10, 13, …

11. VALUES INTEGRATION
A sequence may also refer
to an orderly arrangement of
doing things. Can you share a
recipe of a dish that you cooked
in FT or the procedure you
undertook in making a mini
cabinet in FCM or any step by
step procedure in your respective
specialization?

12. Let’s see if you understood the
lesson...…
Enumerate the steps in
finding the formula of a
sequence bytrial anderror.

13. 1) 2, 5, 8, 11, 14, 17,…
2) 3, 7, 11, 15, 19,…
3) 6, 2, 9, 5, 2,…
4) 2, 4, 6, 8, 10,…
5) -1, ¼, -1/27, 1/256,…
Givetheequation that describesthe following
sequences:

14. ThankYou!