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EXAMPLES & SOLUTIONS
Expressions: Sequence & Patterns
Sequence
A sequence is an ordered set of numbers that form a pattern.
Numbers are discovered from the sequence.
These numbers formulate into a unique rule.
These numbers can aide in discovering a unique pattern.
A sequence that does not follow a pattern has 'NO sequence'.
Each number in the sequence set are called terms.
The sequence of terms are either finite or infinite.
SEQUENCE AND PATTERNS OF NUMBERS
Rule of discovering patterns from a sequence of numbers
Rule:
The sequence numbers correspond to a unique position (1st, 2nd, 3rd, etc.).
Finite sequence:
{ 1, 6, 11, 16, 21, . . nth}
1st
2nd
3rd
4th
5th
nth
Infinite sequence:
{ 1, 6, 11, 16, 21, . . . . . . }
Arithmetic Sequences
Rules of adding and subtracting sequences
Rule:
Arithmetic sequence is when you add or subtract constant or common values from one term to the next.
{-2, 0, 2, 4, 6}
Sequence Starts: -2
Pattern Rule: Add 2 to each number in the sequence
CONSISTENT RULE and COMMON PATTERN
+ 2
+ 2
+ 2
+ 2
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Geometric Sequences
Rules of multiplying and dividing sequence
Rule:
Geometric sequence is when you multiple or divide by a constant value from one term to the next.
{1, 2, 4, 8, . . . . nth}
Sequence Starts: 1
Pattern Rule: Multiply by 2 for each number in the sequence
CONSISTENT RULE and COMMON PATTERN
*2
*2
*2
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
NO Consistent Sequence
Understanding terms with no sequence
Rule:
If there is not a sequence, the pattern of numbers does not add, substract or multiply in a consistent matter.
{8, 2, 0 , 3 . . . . nth}
Sequence Starts: 8
Pattern Rule: Subtract 6 from the first number, subtract 2 to the next number, subtract 3 to the next number, etc. in the sequence
NO CONSISTENT RULE nor COMMON PATTERN
-3
-2
-6
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
8
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