The document discusses numeric patterns, including arithmetic and geometric patterns. Arithmetic patterns have a common difference between consecutive terms, while geometric patterns have a common ratio. Examples are provided of determining the common difference or ratio of patterns and using these to find missing terms or generate additional terms of the pattern. Rules for numeric patterns are also discussed, where the term value is determined by a rule related to the position of the term.

1. NUMERIC PATTERN
GRADE 8
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2. NUMERIC PATTERN
Numeric patterns are commonly divided into
1. Arithmetic (made by adding or subtracting a number each
time).
2. Geometric (which involve multiplying or dividing by a number).
Some geometric patterns are exponential, that is, they are
made by multiplying by an exponent.
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3. ARITHMETIC PATTERNS
The arithmetic patterns are one obtained by adding or
subtracting a constant number all the time. The constant
number is called the common difference.
Example of arithmetic patterns
(a) 2, 4, 6, 8, 10, …,…, …, …, … (can you guess the missing terms?
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4. ARITHMETIC PATTERN CONT.…
From
2, 4, 6, 8, 10, …,…, … The numbers 2, 4, 6, 8, 10 are referred to as
TERMS.
Therefore,
2 is the first term
4 is the second term
6 is the third term
8 is the fourth term
10 is the fifth term etc.
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5. ARITHMETIC PATTERN CONT.…
From
2, 4, 6, 8, 10, …,…, …
The constant difference is obtained by taking the second term minus the first term or
the third minus the second term or fourth minus the third term etc.
The common difference of the pattern above is 2. Thus,
The 2nd term – the 1st term: 4 – 2 = 2 or
The 3rd term – the 2nd term: 6 – 4 = 2 or
The 4th term – the 3rd term: 8 – 6 = 2 etc
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6. ARITHMETIC PATTERN CONT.…
Can you tell the common difference between the terms of the patterns below and
find the next term.
1. 7, 11, 15, 19, 23, 27, … d = _______, the 7th term =_________
2. 5, 13, 21, 29, 37, … d = _______, the 6th term = _________
3. 18, 15, 12, 9, 6, … d = _______, the 6th term =_________
4. 40, 35, 30, 25, … d = _______, the 5th term = _________
Check your
answers
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7. PATTERNS
Which of the following patterns arithmetic?
a) 3, 8, 13, 18, 23, …
b) 11, 17, 23, 29, …
c) 7, 14, 20, 28, 36, …
d) 0, 7, 14, 21, …
e) 48, 43, 40, 31, 27,….
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8. ARITHMETIC PATTERNS
For each of the arithmetic pattern below find the next TWO terms.
a) 100, 103, 106, 1009, __, __.
b) 200, 189, 178, 167, __, __.
c) 30, 37, 44, 51, __, ___.
d) 50.0, 54.3, 58.6, 62.9, __,__,
e) 2, 8, 14, 20, __, ___,
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9. ARITHMETIC PATTERNS
The following are arithmetic patterns
Find the missing term
a) 5, 9, ___, 17, 21, ____, 29.
b) ___, ____, 19, 24, 29, 34.
c) 4, ____, 34, 49, 64, ___, 94.
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10. SUMMARY
We have discussed the arithmetic patterns and you
have noted that THE ARITHMETIC PATTERNS have
the common difference between the consecutive
terms. Using this common difference you can
determine the next few terms of the pattern. [Feel
free to repeat the part for further clarification].
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11. ANSWERS
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12. ARITHMETIC PATTERN ANSWERS
Can you tell the common difference between the terms of the patterns below and
find the next term.
1. 7, 11, 15, 19, 23, 27, … d = _______, the 7th term =_________
2. 5, 13, 21, 29, 37, … d = _______, the 6th term = _________
3. 18, 15, 12, 9, 6, … d = _______, the 6th term =_________
4. 40, 35, 30, 25, … d = _______, the 5th term = _________
4 31
8
-3
-5
45
3
20
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13. PATTERNS ANSWERS
• Which of the following patterns arithmetic?
a) 3, 8, 13, 18, 23, … it is arithmetic
b) 11, 17, 23, 29, … it is arithmetic
c) 7, 14, 20, 28, 36, … it is not arithmetic
d) 0, 7, 14, 21, … it is arithmetic
e) 48, 43, 40, 31, 27,…. it is not arithmetic
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14. ARITHMETIC PATTERNS ANSWERS
For each of the arithmetic pattern below find the next TWO terms.
a) 100, 103, 106, 1009, 112, 115
b) 200, 189, 178, 167, 156, 145
c) 30, 37, 44, 51, 58, 65
d) 50.0, 54.3, 58.6, 62.9, 67.2,71.5
e) 2, 8, 14, 20, 26, 32
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15. ARITHMETIC PATTERNS ANSWERS
The following are arithmetic patterns
Find the missing term
a) 5, 9, 13, 17, 21, 25, 29.
b) 9, 14, 19, 24, 29, 34.
c) 4, 19, 34, 49, 64, 79, 94.
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17. GEOMETRY PATTERN
Geometric patterns are obtained when multiplying or
dividing by a constant term all the time. The common
constant is called common ratio, r.
To get the common ratio is obtained by:-
r=
second term
first term
=
third term
second term
=
fourth term
third term
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18. EXAMPLE
Determine the common ratio of the following geometric
patterns
3, 9, 27, 81, 243, …
Ratio, r =
2nd term
1st term
=
3rd term
2nd term
=
4th term
3rd term
=
5𝑡ℎ
term
4th term
Ratio, r = 9 ÷ 3 = 27 ÷ 9=81 ÷ 27 = 243 ÷ 81 = 3
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19. Determine the ratio of the following patterns
a) 1, 4, 16, 64, 128, …
b) 2, 4, 8, 16, 32, …
c) 81, 27, 9, 3, 1, …
d) -7, -14, -28, -56, …
e) 9, 6, 4, …
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20. Determine the next term of the following geometric
patterns
a) 7, 21, 63, 189, ___.
b) 4, 16, 64, 256, ___.
c) 6, 12, 24, 48, ___.
d) 8, 40, 200, ___.
e) 1, 7, 49, 343, ___.
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21. Determine the ratio of the following patterns
a) 1, 4, 16, 64, 128, … r = 4
b) 2, 4, 8, 16, 32, … r = 2
c) 81, 27, 9, 3, 1, … r = 1/3
d) -7, -14, -28, -56, … r = 2
e) 9, 6, 4, … r = 2/3
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22. Determine the next term of the following geometric
patterns
a) 7, 21, 63, 189, 567.
b) 4, 16, 64, 256, 1024.
c) 6, 12, 24, 48, 96.
d) 8, 40, 200, 1000.
e) 1, 7, 49, 343, 2401.
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24. THE PATTERN RULE
Consider the table 1 below
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Position 1 2 3 4 5 n 25
Term 3 6 9 12 15 3 x n ?
The rule: The position of the term x 3 = n x 3
What is the missing value?
= 25 x 3 = 75

25. THE PATTERN RULE CONT…
Consider the table 2 below.
(a) Develop the rule to generate these terms
(b) Fill the missing term
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Position 1 2 3 4 n
Term 8 16 24
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26. THE PATTERN RULE CONT…
Consider the table 3 below.
(a) Develop the rule to generate these terms
(b) Fill the missing gaps
(c) What is the term in 20th position?
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Position 1 2 3 4 5 n
Term 6 7 8 9
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27. COMPLETE THE TABLE AND THEN STATE THE RULE
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28. COMPLETE THE TABLE AND THEN STATE THE RULE
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Position 1 2 3 4 5 6 n
Term 1 4 9 25
(a) Complete the table
(b) State the rule
(c) What is the term in 12th position?
(d) What is the term in 20th position?

29. SUMMARY
• Geometric patterns have the common ratio
• To get the next term, take the previous term times the ratio
• The pattern rule depends on position of the term
• Generate the terms using the rule developed from the patterns
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30. THE PATTERN RULE - ANSWERS
Consider the table 2 below.
(a) Develop the rule to generate these terms
-You have seen the terms are generated by multiplying the position by 8. So the
rule is 8n. Where n is the position of the term.
(a) Fill the missing gaps: - 4 x 8 = 32
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Position 1 2 3 4 n
Term 8 16 24
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1 x 8 2 x 8 3 x 8 4 x ? ? x ?
nth
rule

31. THE PATTERN RULE CONT…
Consider the table 3 below.
(a) Develop the rule to generate these terms
- You have seen that the terms are generated by adding 5 to the
term’s position. The rule is 5 + n
(a) Fill the missing term: = 5 + 5 = 10
(b)In 20th position the term is 20+5=25
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Position 1 2 3 4 5 n
Term 6 7 8 9
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32. COMPLETE THE TABLE AND THEN STATE THE RULE
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 The table is filled
 The rule is 7 + position; thus 7 + n
32 42 7 + n

33. COMPLETE THE TABLE AND THEN STATE THE RULE
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Position 1 2 3 4 5 6 n
Term 1 4 9 25 n2
(a) Complete the table (completed)
(b) State the rule: n2
(c) What is the term in 12th position? 122 =144
(d) What is the term in 20th position? 202 = 400
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