Generating Sequences

1. GENERATING
SEQUENCES
AND FINDING
RULES FOR
SEQUENCES
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2. Objectives
Generate terms of a linear
sequence using term-to-term
and position-to-term rules
Find term-to-term rules and
position-to-term rules of
sequences
Tujuan Pembelajaran

3. Mathematics is the
art of giving the
same name to
different things.
Henri Poincaré

4. TERM &
TERM-TO-TERM RULE
5, 9, 13, 17, …
What is the first term? The first term is ….
Apakah suku pertamanya? Suku pertamanya adalah 5
What is the second term? The second term is ….
Apakah suku keduanya? Suku keduanya adalah ….
What is the third term? The third term is ….
term
term term
term

5. TERM &
TERM-TO-TERM RULE
5, 9, 13, 17, …
What is the fourth term? The fourth term is ….
What is the next term? ….
What is the 8th term? ….
term
term term
term
5, 9, 13, 17, 21, 25, 29, 33

6. What is the rule when going from one term to the next?
Apa aturan ketika beralih dari satu suku ke suku berikutnya?
the rule when going from one term to the next is ….
So, the term to term rule is ….
TERM &
TERM-TO-TERM RULE
5, 9, 13, 17, …?
+ 4
+ 4
+ 4 + 4

7. 25
22
27
24
29
… ???
What is the next number?
TERM &
TERM-TO-TERM RULE

8. POSITION-TO-TERM RULE
Position number 1 2 3 4
Term 3 6 9 12
Multiples of 3
(Kelipatan 3)
3 6 9 12
3, 6, 9, 12, … (and so on)
Term-to-term rule is add 3
Position-to-term rule is
Term = 3 x position number
3 x 1 = 3 3 x 2 = 6 3 x 3 = 9 3 x 4 = 12

9. POSITION-TO-TERM RULE
Work out the 21st term.
Term = 3 x position number - 4
Anwer:
The 21st term = 3 x 21 - 4
Example:
POSITION-TO-TERM RULE
Example:

10. Write down the first four terms of this sequence:
First term = 3 ; term-to-term rule = add 2
Answer:
…, …, …, …
Example:

11. Lesson Recap
Term = an individual number in a sequence
Term-to-term rule = a rule to find a term of a
sequence, given the previous term
Position-to-term rule = a rule to find a term of
a sequence, look the position number

12. Practice
Write down the first four terms of each
sequence:
A. First term = 2 ; term-to-term rule =
subtract 2
B. First term = 3 ; term-to-term rule =
add 5

13. Practice
Write down the first four terms of each
sequence:
C. First term = -1 ; term-to-term rule = subtract 5
D. First term = -10 ; term-to-term rule = add 20

14. Practice
2. The first term of a sequence is 5.
The term-to-term rule is add 10.
What is the 20th term of a sequence?
Explain how you worked out your answer!

15. Practice
3. Work out the 10th term.
Term = 2 x position number + 3
Anwer:
The 10th term = … x … + …
= …

16. THANK YOU