3. Numbers are not only used for counting or
measuring. It is also used to identify order and
sequences. One good example is the use of
numbers for identifying locations and one’s
addresses. Most addresses follow a certain
process or sequence. There is a good reason why
most streets are named as 1st street, 2nd street,
3rd street, and so on. This makes it easier for us to
locate one’s residence or business address.
4. Numbers, figures, objects, or symbols arranged in a
definite order or sequence is often encountered in
Mathematics. For instance,
5. Numbers in (a), figures in (b) and letters in (c) are
arranged in a definite order. Using the given
sequences:
What is the next number in (a)?
Notice that the next number will be obtained by
adding 2 to the previous number. The next
number on the pattern is 18
6. What is the next figure in (b)?
Observe that the shaded triangle is
rotating clockwise around the
square. Therefore,
the next figure is
7. Instruction: Supply the next three letters, figures,
symbols, or combination of numbers and letters in
the following patterns.
1. A, C, E, G, I, …
__ __ __
2. 3, 6, 9, 12, …
__ __ __
3.
8. Find the missing number and state the pattern.
1. 512, 128, _____8
2. 243, _____ 27, 9
3. 10, 17, ____ 31
4. 6, 10, ____ 21
5. 17, 27, 37
11. Find the missing term in each pattern.
1. 8, 15, 22, __ 36, 43
2. ___, 65, 59, 53, 47, 41
3. 17, __ 23, 26, 29, 32
12. A sequence is a set of numbers written in a special
order by the application of a
definite rule.
• Each number in a sequence is called a term.
• To formulate the rule in finding the nth term of a
sequence, we can look for a pattern.
14. Formulate the rule in finding the nth term for each
sequence. Use counting numbers to easily
find the rule.
15. COUNTING NUMBERS
The set of numbers 1, 2, 3, 4, … without 0 (zero) is
called counting numbers.
Since the rule of the sequence is adding 1 to the
preceding number to be able to get the next term
(s),the nth term rule for this sequence is n + 1.
16. Instruction: Supply the next three letters, figures,
symbols, or combination of numbers and letters in
the following patterns.
17. Fill in the missing terms in the given sequence.
18. Read each item carefully.
1. 11, 12, 13, 14, 15, …Which nth rule
applies for?
2. The nth rule for this sequence 2, 7,
12, 17, … is ________
20. Study the sequence below.
1. Find the nth term rule.
2. Solve for the 20th term and 35th term.
21. In the sequence 3, 5, 7, 9 it starts at 3 and jumps 2 every time.
So, what can a rule for 3, 5, 7, 9,…be?
Firstly, we can see the sequence goes up 2 every time, so we can
guess that a
Rule is something like "2 times n" (where "n" is the term number).
22. That nearly worked ... but it is too low by 1 every time, so let us try
another one:
The rule is exact for all the terms. So, the nth rule for this sequence is 2
x n + 1 or 2n + 1. Now, we can solve for the 20th term and 35th term.
24. Group Activity each group will fill the blanks in the box.
G1 G2 G3 G4 G5 G6
27. Think Pair Share
Guide Questions:
1. Write down the next two terms of the sequence.
2. Write down an expression for the nth term of this sequence.
3. Work out the 25th term and 50th term of the sequence.
Look at the following sequences.
28. • From looking at the sequence we
can see that each term is 6 larger
than the previous term. We say the
term-to-term rule is “add 6”.
Therefore, the next two terms are 34
and 40.
29. The nth term of a sequence is always written in the form
of “? n+?”. The number in front of the “n” is always the
difference to get from one term to the next. Since
the difference is 6, the first part of our rule will be “6n”.
The rule follows the six times table: 6, 12, 18, 24, 30.
Now compare the 6 times table with our rule:
30. The numbers in the sequence are always 2
less than the 6 times table so we
“adjust” our rule by subtracting 2. (ex. 6 – 4 =
2, 12 – 10 =2… etc.). Now,
putting this together gives nth term = 6n – 2
31. Now we know the nth term = 6n – 2 we just need to substitute n = 25
and 50 to find the 25th term and 50th term of the sequence
32. • Working backward, you will notice a pattern that
subtracts 3 to get the next term
on the left. So, the rule (nth term) will start with 3n.
In our example of 3n, the sequence would be 3, 6, 9, 12,
15. We have just to compare this to the sequence we
have.
3n = 3 6 9 12 15
Our sequence is = 2 5 8 11 14
We can see that every term in 3njust needs to have 1
subtracted to become our sequence, so we subtract
this on to the end of our expression and there we
have it! The nth term of the sequence is 3n – 1.
33. Think Pair Share:
Every year, Mang Ramon’s kinalabaw mango tree
produces 2 more kilos of mangoes than the previous
year. If 25 kilos were harvested in the year 2017, how
many kilos did it produce in 2012? What was the total
number of kilos of mangoes that the tree produces from
2012 to 2017? Formulate the nth rule.
34. 1. What is asked?
The number of kilos of mangoes the tree will
produce in 2012.
The total number of kilos of mangoes the tree will
produce from year 2012
to 2017.
Formulate the nth rule.
2. What are given?
25 kilos in 2017 (starting year)
2 more kilos of mangoes than the previous year
