Question

assignment
katherine period 2 homework

use a separate piece of paper for your journal entry.

journal
explain why all sequences
represent functions.
remember
a sequence is a pattern involving an ordered
arrangement of numbers, geometric figures, letters, or
other objects. it is a function whose domain is the set of
natural numbers.
practice

consider the three sequences given. for each sequence, describe the pattern.

then, represent the sequence as a numeric sequence and as a table of values.
1 matchstick mayhem
three geometric figures
table with term number (1,2,3,4,5,6) and term value (4,15,24,31,36,39) with handwritten notes
4,15,24,31,36,39
2 hancox homes
hancox homes is a popular construction company that builds affordable housing. when the
company first started, they sold 1 home the first month, 3 homes the second month, 9 homes
the third month, and 27 homes the fourth month.
table with term number (1,2,3,4,5,6) and term value (21, 21, 18, 15, 12, 9) with handwritten notes

Explanation:

Journal Question:

A sequence is defined as a function with a domain of natural numbers (positive integers: 1,2,3,...). For every natural number input (term number), there is exactly one corresponding term value in the sequence. This satisfies the core definition of a function: each input has exactly one output.

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1. Matchstick Mayhem

Step1: Identify pattern

Start at 4. Each subsequent increment decreases by 2: $15-4=11$, $24-15=9$, $31-24=7$, $36-31=5$, $39-36=3$.

Step2: Numeric sequence

List term values in order: $4, 15, 24, 31, 36, 39$

Step3: Table of values

Map term numbers to values:

Term Number	1	2	3	4	5	6

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2. Hancox Homes

Step1: Identify pattern

Each term is 3 times the prior term: $3=1\times3$, $9=3\times3$, $27=9\times3$.

Step2: Calculate terms 5 and 6

Term 5: $27\times3=81$; Term 6: $81\times3=243$

Step3: Numeric sequence

List term values in order: $1, 3, 9, 27, 81, 243$

Step4: Table of values

Map term numbers to corrected values:

Term Number	1	2	3	4	5	6

Answer:

Journal Answer:

A sequence is a function because its domain is the set of natural numbers, and each term number (input) corresponds to exactly one term value (output), satisfying the definition of a function.

1. Matchstick Mayhem

• Pattern: Starts at 4, each increment is 2 less than the previous increment (11, 9, 7, 5, 3).
• Numeric Sequence: $4, 15, 24, 31, 36, 39$
• Table of Values:

Term Number	1	2	3	4	5	6

2. Hancox Homes

• Pattern: Each term is 3 times the previous term (geometric sequence with common ratio 3).
• Numeric Sequence: $1, 3, 9, 27, 81, 243$
• Table of Values:

Term Number	1	2	3	4	5	6